Perform the indicated operation.
40−4
010
001
−8
−1
3
⇒ 40
⇒ 0
010
001
⇒ 4
−1
3
Multiply row 1 by the reciprocal of 4.
400
010
001
4
−1
3
100
010
001
−1
3
Answers
Answer:
yeah the answer is in the question just needed the points
Step-by-step explanation:
\(\begin{bmatrix}4 & 0 & -4& |& -8 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\text{4R3+R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{4} & \bold{0} & \bold{0}& |& \bold{4} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)
and,
\(\begin{bmatrix}4 & 0 & -4& |& 4 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\frac{1}{4} \text{R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{1} & \bold{0} & \bold{0}& |& \bold{1} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)
What is matrix?"A set of numbers arranged in rows and columns so as to form a rectangular array."
What is augmented matrix?"A matrix formed by combining the columns of two matrices to form a new matrix."
What are elementary row operations?"The mathematical operations that are performed on rows of a matrix."
For given question,
We have been given an augmented matrix.
\(\begin{bmatrix}4 & 0 & -4& |& -8 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)
We need to perform the row operation 4R3 + R1 → R1
To perform above row operation,
- First multiply the third row by 4. (\(4R_3\))
- Add the new third row (4\(R_3\)) with the first row.
- Then replace Row 1 with the result.
The resultant augmented matrix would be,
\(\begin{bmatrix}\bold{4} & \bold{0} & \bold{0}& |& \bold{4} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)
That is,
\(\begin{bmatrix}4 & 0 & -4& |& -8 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\text{4R3+R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{4} & \bold{0} & \bold{0}& |& \bold{4} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)
Now, we need to perform the row operation \(\frac{1}{4}\) R1 → R1 on the above resultant augmented matrix.
To perform above row operation,
- Multiply the Row 1 by the reciprocal of 4.
- Then replace Row 1 with the result.
The resultant augmented matrix would be,
\(\begin{bmatrix}4 & 0 & -4& |& 4 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\frac{1}{4} \text{R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{1} & \bold{0} & \bold{0}& |& \bold{1} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)
Therefore,
\(\begin{bmatrix}4 & 0 & -4& |& -8 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\text{4R3+R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{4} & \bold{0} & \bold{0}& |& \bold{4} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)
and,
\(\begin{bmatrix}4 & 0 & -4& |& 4 \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix} \xrightarrow{\frac{1}{4} \text{R1}\rightarrow \text{R1}} \begin{bmatrix}\bold{1} & \bold{0} & \bold{0}& |& \bold{1} \\0 & 1 & 0& |& -1 \\0 & 0 & 1& |& 3\end{bmatrix}\)
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Related Questions
Give your vector u = (-1,3) and v = (2,-2), find a linear combination of the vectors u and v of the form au+bv that would result in the vector (5,-3)
Answers
The linear combination of the form au+bv that would result in the vector (5,-3) is given as follows:
4u + 4.5v.
How to obtain the linear combination?If the linear combination is true, we have that:
a(-1,3) + b(2, -2) = (5, 3).
Hence the system of equations is given as follows:
-a + 2b = 5.3a - 2b = 3.From the first equation, we have that:
a = 2b - 5.
Replacing into the second equation, the value of b is given as follows:
3(2b - 5) - 2b = 3
6b - 15 - 2b = 3
4b = 18
b = 4.5.
Hence the value of a is of:
a = 2 x 4.5 - 5
a = 4.
Then the linear combination is:
4u + 4.5v.
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What is the coefficient of determination for a linear model fitting the following bivariate dataset?
Answers
The coefficient of determination for a linear regression model fitting with bivariate dataset ( scatterpot present in above figure) is equals to the 90.097.
When we study about linear regressions, usually analyze two coefficients that help us to know about the quality of the regression model and strength of linear relationship between the variables. One is called the coefficient of determination, denoted by R². Consequently, by observing a scatter plot, we can estimate the value of these coefficients. We have a scatterpot for a linear model fitting of the bivariate dataset is present in above figure. Coefficient of determination is always positive. When data are very closely arranged along a approximate line, then coefficient of determination is more near to 1 (In percentage it is 100). Here points are almost closely arranged . So percentage should be near to 100. So possible answer is 90.097. Hence, the answer is 90.097.
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Complete question :
The above figure complete the question.
What is the coefficient of determination for a linear model fitting the following bivariate dataset?
Are the lines of equations
x = −2 + 2t, y = −6, z = 2 + 6t and
x=−1+t,y=1+t,z=t, t∈ R, perpendicular to each other?
Answers
The given lines of equations are not perpendicular to each other. Therefore, `θ = cos⁻¹(8/(4√10))` which is approximately `28.07°`.Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.
Given lines of equations:
x = −2 + 2t, y = −6, z = 2 + 6tx=−1+t,y=1+t,z=t, t∈ R.
Firstly, we need to find the direction vectors of the two given lines.For the first equation,Let `t=1`, then the point on the line is `(-2+2(1), -6, 2+6(1))`=`(0, -6, 8)`.
Let `t=2`, then the point on the line is
\(`(-2+2(2), -6, 2+6(2))`=`(2, -6,\)14)`.T
herefore, direction vector `
\(v1 = (2, -6, 14)-(0, -6, 8)`=`(2, 0, 6)`\)
For the second equation, direction vector \(`v2 = (1, 1, 1)`.\\\)
Let the angle between the direction vectors `v1` and `v2` be `θ`.
Then, we know that `v1 • v2 = |v1||v2| cosθ`, where `•` represents the dot product of the vectors, and `|.|` represents the magnitude of the vector.
Thus, we have:
(2, 0, 6) • (1, 1, 1) = √(2²+0²+6²)√(1²+1²+1²) cosθ
=> 8 = √40√3 cosθ=> cosθ = 8/(4√10)
Therefore,
`θ = cos⁻¹(8/(4√10))`
which is approximately `28.07°`.
Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.
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During which phase of the systems life cycle are users trained to use the new system?
Answers
Answer:
Step-by-step explanation:
The phase of the systems life cycle during which users are trained to use the new system is called the implementation phase. In this phase, the new system is installed and made operational, and users are trained on how to use it effectively. This phase typically follows the design and development phases and precedes the maintenance phase.
What is the main focus of the implementation phase in the systems life cycle?
The main focus of the implementation phase is training users to use the new system effectively. This includes installing the system and making it operational, as well as providing necessary support and training to ensure users are able to utilize the system efficiently.
The phase of the systems life cycle during which users are trained to use the new system is the implementation phase. This is the phase where the new system is actually implemented and made available for use by the users. It is important to provide training to users during this phase so that they are able to effectively use the new system and understand its functionality.
Therefore, users are trained to use the new system during the implementation phase.
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The implementation phase of the systems life cycle is the time when users are taught how to utilize the new system.
The new system is installed, made operational, and users are instructed on how to utilize it efficiently during the implementation phase. In most cases, this phase comes after the design and development phases and comes before the maintenance period.
Why is user training important during the implementation phase of the systems life cycle?
User training is important during the implementation phase of the systems life cycle because it ensures that users are able to effectively use the new system and understand how it works. This is essential for the successful adoption and utilization of the system by the organization. Without proper training, users may struggle to use the system effectively, leading to reduced productivity and potentially even causing issues with data accuracy and integrity. By providing thorough user training, organizations can ensure that their employees are able to use the new system efficiently and effectively, leading to a successful implementation.
The implementation phase of the systems life cycle is the time when users are taught how to utilise the new system. In this stage, the new system is really put into use and made accessible to users. During this stage, it's crucial to give users training so they can utilize the new system correctly and comprehend its functions.
Therefore, during the implementation phase, users are instructed on how to utilize the new system.
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Hi I need a fit of help with this question!
Answers
Explanation
The unit rate os obtained as shown as follows:
\(\text{Unit rate = }\frac{change\text{ in dollars}}{\text{change in hours}}\)\(\text{Unit rate= }\frac{17\text{dollars}}{\text{hour}}=\text{ 17\$/h}\)Answer is A. The unit rate is equal to $17.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPO
Answers
Answer:
2
Step-by-step explanation:
trust me it's 2 but I'm not for sure
Explanation: it’s 2
Marisa has $26 in her purse. She pays $5 for lunch. Which expression represents this situation?
a.
–26 + (–5)
b.
–26 + 5
c.
26 + (–5)
d.
26 + 5
Answers
I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS CORRECTLY
Which mathematical sentence is a correct translation of the problem, where c represents the variable "original amount in checking account?"
Franklin just deposited $364 into his checking account. If Franklin now has a total of $500 in his account how much did he have originally?
O A. C+ 364 = 500
O B. C + 364 > 500
O C. C-364 > 500
O D. C + 500 = 364
O E. C-500 = 364
O F. C = 500
Answers
Answer:
D c+364=500
Step-by-step explanation:
Answer:
A. C + 364 = 500
Step-by-step explanation:
HeLP with this question please put the answer on a point
Answers
Answer:
\(x = -1\)
\(y = 3\)
Step-by-step explanation:
Given
The attached table
Required
Fill in the blanks
First, we need to calculate the slope
\(m = \frac{y_2-y_1}{x_2-x_1}\)
Where:
\((x_1,y_1) = (1/2,1)\)
\((x_2,y_2) = (3,-9)\)
So, we have:
\(m = \frac{-9-1}{3-1/2}\)
\(m = \frac{-10}{3-0.5}\)
\(m = \frac{-10}{2.5}\)
\(m = -4\)
Next, we calculate the equation:
\(y - y_2 = m(x - x_2)\)
This gives:
\(y - (-9) = -4(x - 3)\)
\(y +9 = -4(x - 3)\)
\(y +9 = -4x +12\)
Make y the subject:
\(y = -4x +12-9\)
\(y = -4x +3\)
So,
When y = 7:
We have:
\(y = -4x +3\)
\(7 = -4x +3\)
Collect Like Terms
\(4x = 3 - 7\)
\(4x = -4\)
Divide through by 4
\(x = -1\)
When x = 0, we have:
\(y = -4x +3\)
\(y = -4 * 0 + 3\)
\(y = 0 + 3\)
\(y = 3\)
Find the slope of the line that passes through the pair of points (4,3) and (-2, 6)
Answers
Answer: (6,9)
Step-by-step explanation:
Add them both up
\(\frac{3}{-6}\)Answer:
Slope = \(\frac{3}{-6}\) or -0.5
Step-by-step explanation:
Slope formula: \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
( 4, 3 )
( -2, 6)
\(\frac{6-3}{-2-4}\) = \(\frac{3}{-6}\) = -0.5
Slope = \(\frac{3}{-6}\) or -0.5
How many numbers between 1 and 200 are divisible by 4 or 6?
Answers
Between 1 and 200, there are 66 numbers that are divisible by either 4 or 6.
To find the numbers between 1 and 200 that are divisible by 4 or 6, we need to determine the count of numbers divisible by 4 and the count of numbers divisible by 6, and then subtract the count of numbers divisible by both 4 and 6 (since they would be counted twice).
Divisibility by 4:
To find the count of numbers divisible by 4, we divide 200 by 4 and round down to the nearest whole number. So, 200 divided by 4 equals 50, meaning there are 50 numbers divisible by 4 between 1 and 200.
Divisibility by 6:
Similarly, to find the count of numbers divisible by 6, we divide 200 by 6 and round down. 200 divided by 6 equals approximately 33.33, so there are 33 numbers divisible by 6 between 1 and 200.
Numbers divisible by both 4 and 6:
To find the count of numbers divisible by both 4 and 6, we need to find the count of numbers divisible by their least common multiple, which is 12. We divide 200 by 12 and round down, resulting in approximately 16.67. Thus, there are 16 numbers divisible by both 4 and 6 between 1 and 200.
Finally, we add the count of numbers divisible by 4 and the count of numbers divisible by 6 and subtract the count of numbers divisible by both 4 and 6 to get the total count of numbers divisible by either 4 or 6. Therefore, there are 50 + 33 - 16 = 67 numbers between 1 and 200 that are divisible by either 4 or 6.
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HELP URGENT ASAP WILL MARK AND 5 STARS DUE in 5 MINUETS HURRY
Answers
Answer:
1. x=8
the other ones i got was decimals and i dont think you want those for this assignment
Step-by-step explanation:
How many kilometers is it from the main gate to Manatee Springs? (Hint: To convert from
yards to kilometers, multiply by 0.0009144). Round answer to the nearest hundredth kilometer
Manatee Springs
Elephant
House
3,500 yds
- 200 yds
Tran Depot
2000
Bird Sanctuary
Main Gate
(SHOW WORK)
Answers
Answer:
6.04 km
Step-by-step explanation:
From the image attached, both triangles form are similar to each other because their corresponding angles are equal, therefore they are equiangular triangles. equiangular triangles have the same shape but different sizes and the ratio of their corresponding sides are equal.
Therefore since their corresponding sides are equal we can calculate the distance from the main gate to Manatee Springs. It is given by:
\(\frac{3500\ yards}{2000\ yards} = \frac{4200\ yards}{x}\\ x= \frac{4200\ yard*2000\ yards}{3500\ yards}=2400\ yards\)
x = 2400 yards.
The distance from the main gate to Manatee Springs = x + 4200 yards = 2400 + 4200 = 6600 yards
The distance from the main gate to Manatee Springs = 6600 yards = (6600 * 0.0009144) km = 6.04 km
The distance from the main gate to Manatee Springs = 6.04 km
Help pleaseeeee??????????????
Answers
Answer:
x=3
Step-by-step explanation:
The whole line (DF) equals 9x - 39. So you need to make that equal to 47+3x+10 and work out like so. I hope this helps!
Andrew rents bowling shoes for $4. He bowls 2 games. Andrew spent a total of $22. How much was the cost of each game, b? Complete the bar diagrams, and then solve the problem. Three bar graphs. Top bar on each is Total Spent. Bottom bar on each has 3 sections. The left section is labeled shoe rental, and each of the other sections is labeled cost per game. The cost per game sections are b. The other parts have fill-in boxes. Each game cost .
Answers
Answer:
2b + 4 = 22
b= 9, the cost of each game is $9
Step-by-step explanation:
(4 points) Problem #1. Record the answers to problem 6.80 in the textbook. a) Zo.20 = b) 20.06 = (2 points) Problem #2. Record the answer to problem 6.81 in the textbook. and The two Z-scores are 28
Answers
A Z-score represents how many standard deviations an individual data point is from the mean of a dataset. The formula for calculating a Z-score is:
Z = (X - μ) / σ
Where:
- Z is the Z-score
- X is the individual data point
- μ (mu) is the mean of the dataset
- σ (sigma) is the standard deviation of the dataset
If you can provide the data or statistics needed, I'd be more than happy to help you calculate the Z-scores for the given problems.
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Stock was selling at $25 a share. A month later it was selling at $30 a share what is the percent increase
Answers
Answer: 20%
Step-by-step explanation:
How would you solve this problem step by step ?
4√15(2√2 + √5)
Answers
\(~~4\sqrt{15} \left( 2\sqrt 2 + \sqrt 5 \right)\\\\=8\sqrt{15} \sqrt 2 + 4\sqrt{15} \sqrt 5\\\\=8\sqrt{15\times 2}+4 \sqrt{15 \times 5}\\\\=8\sqrt{30}+4\sqrt{3 \times 5 \times 5}\\\\=8\sqrt{30} + 4 \sqrt{3\times 5^2}\\\\=8\sqrt{30} + 4\cdot 5 \sqrt 3\\\\=8\sqrt{30} +20\sqrt{3}\)
show that 3x4 1 is o(x4∕2) and x4∕2 is o(3x4 1).
Answers
3\(x^4\) + 1 is equivalent to \(x^{(4/2)}\) in terms of asymptotic growth rate. The value of 3\(x^4\) + 1 is O(\(x^{(4/2)}\)) and \(x^{(4/2)}\) is O(3\(x^4\) + 1).
To show that 3\(x^4\) + 1 is O(\(x^{(4/2)}\)), we need to find a constant C and a value of x such that:
|3\(x^4\) + 1| <= C|\(x^{(4/2)}\)|
For x >= 1, we can say that:
3\(x^4\) + 1 <= 4\(x^4\)
Taking the square root of both sides, we get:
sqrt(3\(x^4\) + 1) <= 2x²
Thus, we can choose C = 2 and x0 = 1, and we have:
|3\(x^4\) + 1| <= 2|\(x^{(4/2)}\)| for all x >= 1
Therefore, 3\(x^4\) + 1 is O(\(x^{(4/2)}\)).
To show that \(x^{(4/2)}\) is O(3\(x^4\) + 1), we need to find a constant C and a value of x such that:
|\(x^{(4/2)}\)| <= C|3\(x^4\) + 1|
For x >= 1, we can say that:
\(x^{(4/2)}\) <= x²
Thus, we can choose C = 1 and x0 = 1, and we have:
|\(x^{(4/2)}\)| <= |3\(x^4\) + 1| for all x >= 1
Therefore, \(x^{(4/2)}\) is O(3\(x^4\) + 1).
Since both 3\(x^4\) + 1 is O(\(x^{(4/2)}\)) and \(x^{(4/2)}\) is O(3\(x^4\) + 1).
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Dylan invested some money in his bank.
He agreed a simple interest rate of 3% per annum fo a period of 2 years.
At the end of the 2-year period the value of his investment increased by £72
Work out the value of Dylan's initial investment
Answers
The amount invested by Dylan will be £1200.
What is simple interest?Simple interest is the amount of borrowing-related interest that is calculated using only the original principal and a constant interest rate.
Given that Dylan invested some money in his bank. He agreed on a simple interest rate of 3% per annum for a period of 2 years. At the end of the 2-year period, the value of his investment increased by £72.
The amount of money invested will be calculated as,
SI = ( P x R x T ) / 100
72 = ( P x 3 x 2 ) / 100
7200 = 6P
P = 7200 / 6
P = £1200
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is it possible to choose (2n 1)^2 points in the disc of radius n such that the distance between any two of them is greater than 1?
Answers
Answer: its (4f 5) ^3
Step-by-step explanation:
hello pls fill in the question marks :) Multiply (x + 1)^3
(x + 1)^3= (x + 1)(x + 1)^2
= (x + 1)(x^2 + 2x + 1)
= x3 + ?x^2 + ?x + ?
Answers
Answer: 3, 3, 1
Step-by-step explanation:
(x+1)³= (x+1)(x+1)²
=(x+1)(x²+2x+1)
=x³+ 3x²+3x+1
please i need the answer with steps
Answers
Answer:
= (9/4) + (17/6)
= (61/12) / 2
= 61/24
Hope this helps you. Do mark me as brainliest.
solve m = 10x - x for x
Answers
Answer:
X = M/9
Step-by-step explanation:
In a market survey, 100 traders sell fruits, 40 sell apples, 46 oranges, 50 mangoes. 14 apples and oranges. 15 apples and mangoes, and 10 sell the three fruits. Each of the 100 traders sells at least one of the three fruits. Find the number that sell oranges and mangoes only.
Answers
The number of traders that sell oranges and mangoes only are 17.
How to determine the common differenceSince there are three sets, use the formula
n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)
A represents apple traders = 40
O represents orange traders = 46
M represents mangoes traders = 50
A∪O∪M = total traders = 100
A∩O = 14
O∩M = ?
A∩M = 15
A∩O∩M = 10
Substitute values into the formula
100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10
100 = 146 - 29 - O∩M
100 = 117 - O∩M
Make O∩M subject of formula
- O∩M = 100 -117
O∩M = 17 traders
Therefore, the number of traders that sell oranges and mangoes only are 17.
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Help me please! I’ve been stuck on this forever:(
Answers
Positive
( -1/6 ) ( -2 ) ( -3/5 ) ( -9 )
( 3 ) ( -3 ) ( -3 ) ( -3 ) ( -3 )
( -2 3/4 ) ( -1 1/5 )
----------------------------------------------------------------------------------------------------------------
Negative
( -4/9 ) ( 7/4 )
( -4/7 ) ( -3/5 ) ( -9 )
( -10/7 ) ( 8/3 )
----------------------------------------------------------------------------------------------------------------
Hope this helps! <3
Which of the following is considered a biased estimator?
variance
proportion
median
mean
Answers
Answer:
Variance
Step-by-step explanation:
Biased estimators ar ethe values in which the calculated value is less than the estimated values .
For statistics sector this word is used.
Mean and medians are standards and unbiased estimators .
Option A
In between: variance, proportion, median and mean, variance is considered a biased estimator.
What is a biased estimator?An estimate that deviates from the genuine population value is said to be biased. If the kind and extent of the bias are known, a biased sample may still be informative. When a sample's value matches the actual value of a population parameter, that is an unbiased estimator.
Because they are centered on parameters, the sample percentage (p) and sample mean (x) are both unbiased estimators.
When the population is normal, the sample median is a fair estimate of the population median. It is untrue that the sample median is a fair estimator of the population median for a broad population, nevertheless. When the population is not symmetric, the sample mean is a biased estimator of the population median.
A biased estimate of the population variance is the sample variance.
Therefore, a biased estimator is variance.
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After how much time to the nearest minute Will the cost of plan a be equal to the cost of plan b
Answers
Let
y ----> total charge in a month
x ----> number of minutes
so
Plan A
y=0.21x+11
Plan B
y=0.10x+20
Equate both equations
0.21x+11=0.10x+20
solve for x
0.21x-0.10x=20-11
0.11x=9
x=9/0.11
x=81.82 minutes
Convert to hours and minutes
81.82 minutes=60+21.82=1 hour 22 min
therefore
the answer is option A4. If a runner completed a 100 meter dash with a time of 13.75 seconds what is the runners speed? Velocity?
Answers
Speed is given by Distance/ Time taken
\(\begin{gathered} \text{speed =}\frac{Dis\tan ce}{Time\text{ }}\text{ =}\frac{100\text{ m}}{13.75\text{ s}} \\ \text{Speed = 7.27m/s } \end{gathered}\)The Velocity is 7.27m/s in the direction of the runner
Adam spent $25 for 5 pizzas how much money does he need to buy 7 pizzas
Answers
$35
He would need $35 to buy 7 pizzas because if you divide 25 and 5, you would get 5.
5+5+5+5+5+5+5=35
5x7=35
Answer:
$35
Step-by-step explanation:
So basically to find the unit price we need to craft an equation. Lets imagine one pizza is p.
We can craft this equation:
5p = 25
Divide both sides by 5
p = 5
How we just multiply that unit price by 7 to get 35, which is the answer
I put a lot of thought and effort into my answers, so I would really appreciate a Brainliest!