First if is an Eigenvector of the matrix A with Eigenvalue 4, will also be an Eigenvalue for any linear combination of the matrix A.
Answers
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.
What is matrix?
A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.
The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.
When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.
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Related Questions
The coordinates of the point 3/10 of the way from A(-3,-8) to B(11,4) are ___?
Answers
Answer:
The coordinate of the point 3/10 of the way from A to B = (0.5, -4.4)
Step-by-step explanation:
to calculate the point 3/10 of the way from A to B, let us first find the difference in the coordinates of the point
Change in x coordinate: x₁ = -3, x₂ = 11
= x₂ - x₁ = 11 - (-4) = 11 + 4 = 15
3/10 of 15 = 0.3 × 15 = 4.5
This means that the point on the x axis is 4.5 points away from x₁
= -4 + 4.5 = 0.5
Change y coordinate: y₁ = -8, y₂ = 4
= y₂ - y₁ = 4 - (-8) = 4 + 8 = 12
3/10 of 12 = 0.3 × 12 = 3.6
This means that the point on the y axis is 3.6 points away from y₁
= -8 + 3.6 = -4.4
Therefore the coordinate of the point 3/10 of the way from A to B = (0.5, -4.4)
if I worked and made 500000 a year how much would I make each month??
Answers
500,000 / 12 = 41,666.66
To make half a million a year, one must make about 41,666 dollars per month.
Step 3: Write the equation of the line that passes through the point (4,−1)
(
4
,
−
1
)
that is parallel to the line 2−3=9
Answers
Answer:
-
Step-by-step explanation:
-
24°
Solve for c.
= [?]°
C =
60% C
Enter
![24Solve for c.= [?]C =60% CEnter](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/18LkggivbR7cp80IPjukTXssaWPx5XaX.png)
Answers
Answer:
96°
Step-by-step explanation:
You want the value of angle C in the diagram with two parallel lines and a triangle between them.
Angle sum theoremThe sum of angles in a triangle is 180°, so the missing angle in the triangle is ...
180° -60° -24° = 96°
Alternate interior anglesAngle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:
C = 96°
<95141404393>
find the sum 4/V3 + 11/V12
Answers
The sum 4/V3 + 11/V12 is equal to \(\frac{4v^9+11}{v^{12}}\).
We have given that,
\(\frac{4}{v^3}+\frac{11}{v^{12}}\)
\(=\frac{4v^9}{v^{12}}+\frac{11}{v^{12}}\)
List common multiplier of the V^3 and V^12 is V^12.
adjust the fraction based on List common multiplier.
What is the fraction rule?
\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}\)
Therefore we get the,
\(=\frac{4v^9+11}{v^{12}}\)
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Keller Construction is considering two new investments. Project E calls for the purchase of earthmoving equipment. Project H represents an investment in a hydraulic lift. Keller wishes to use a net present value profile in comparing the projects. The investment and cash flow patterns are as follows: Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods.
Answers
Based on the net present value profile, Project H has a higher NPV than Project E.
To compare the net present value (NPV) of Project E and Project H, we need to calculate the present value of cash flows for each project and determine which one has a higher NPV. The cash flow patterns for the two projects are as follows:
Project E:
Initial investment: -$100,000
Cash flows for Year 1: $40,000
Cash flows for Year 2: $50,000
Cash flows for Year 3: $60,000
Project H:
Initial investment: -$120,000
Cash flows for Year 1: $60,000
Cash flows for Year 2: $50,000
Cash flows for Year 3: $40,000
To calculate the present value of cash flows, we need to discount them using an appropriate discount rate. The discount rate represents the required rate of return or the cost of capital for the company. Let's assume a discount rate of 10%.
Using the formula method, we can calculate the present value (PV) of each cash flow and sum them up to obtain the NPV for each project:
For Project E:
PV = $40,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $60,000/(1 + 0.10)^3
PV = $36,363.64 + $41,322.31 + $45,454.55
PV = $123,140.50
For Project H:
PV = $60,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $40,000/(1 + 0.10)^3
PV = $54,545.45 + $41,322.31 + $30,251.14
PV = $126,118.90
Using the financial calculator method, we can input the cash flows and the discount rate to calculate the NPV directly. By entering the cash flows for each project and the discount rate of 10%, we find that the NPV for Project E is approximately $123,140.50 and the NPV for Project H is approximately $126,118.90.
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Find the equation of the line in standard form that passes through the following points. Eliminate anyfractions and simplify your answer.(4, -8) and (9, 11)
Answers
We want to find the equation of the line that passes through the points:
(4 , -8) and (9 , 11)
First, we're going to find the slope between these points using the fact that:
If we have two points that lie on a line:
\((x_1,y_1)\text{ and }(x_2,y_2)\)The slope between them can be found using the formula:
\(m=\frac{y_2-y_1}{x_2-x_1}\)If we replace our values:
\(\begin{gathered} (x_1,y_1)=(4,-8) \\ (x_2,y_2)=(9,11) \\ x_1=4 \\ x_2=9 \\ y_1=-8 \\ y_2=11 \end{gathered}\)The slope will be:
\(m=\frac{11-(-8)}{9-4}=\frac{11+8}{5}=\frac{19}{5}\)Now, we could apply the point-slope equation. This equation tells us that we can find the equation of the line if we got a point (x1,y1) on the line, and the slope m:
\(y=y_1+m(x-x_1)\)Replacing our values:
\(\begin{gathered} y=-8+\frac{19}{5}(x-4) \\ y=-8+\frac{19}{5}x-\frac{76}{5} \\ y=\frac{19}{5}x-\frac{116}{5} \end{gathered}\)This, is the general form. We want to express the last equation as a standard form like this:
\(Ax+By=C\)If we re-write:
\(\begin{gathered} y=\frac{19x-116}{5} \\ \\ 5y=19x-116 \\ 19x-5y=116 \end{gathered}\)Therefore, the standard for the equation of the line that passes through (4 , -8) and (9, 11) is:
19x-5y=116
CAN SOMEONE HELP WITH THIS PROBLEM?
Answers
The value of the infinite series expression \(\sum^{124}_{i = 1}(29a_i - 13b_i) \\\) is -30.
Given information:
\(\sum^{124}_{i = 1}a_i = -10\) and \(\sum^{124}_{i = 1} b_i = -20\).
The required series form can be rearranged as,
\(\sum^{124}_{i = 1}(29a_i - 13b_i) &= 29\sum^{124}_{i = 1}a_i - 13\sum^{124}_{i = 1}b_i\)
Substitute the provided values of \(\sum^{124}_{i = 1}a_i = -10\) and \(\sum^{124}_{i = 1} b_i = -20\).
We get,
\(\sum^{124}_{i = 1}(29a_i - 13b_i) \\\) = 29(-10) - 13(-20)
\(\sum^{124}_{i = 1}(29a_i - 13b_i) \\\) = -290+ 260
\(\sum^{124}_{i = 1}(29a_i - 13b_i) \\\) = -30.
As a result, the required value is -30.
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Virginia polled a large sample of individuals to find the percentage of students with known food allergies and the percentage of students without known food allergies. Which of the following could sufficiently display the data if only the two given categories are to be included?
Select the correct answer below:
bar graph
pie chart
either a pie chart or a bar graph
neither a pie chart nor a bar graph
Answers
The following could sufficiently display the data if only the two given categories are to be included is either a pie chart or a bar graph.
Any chosen person may fall into one of the categories. Consequently, a bar graph or a pie chart might both depict the data effectively.
So, the choice is between a pie chart and a bar graph.
In order to show mathematical issues, the "pie chart," often referred to as a "circle chart," divides the circular statistical visual into sectors or portions. A proportionate amount of the entire is indicated by each sector. The Pie-chart is now the most effective method for determining the composition of something.
Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.
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What are the mean and the median for the data set below? 2, 4, 6, 4, 3, 5, 6, 9, 3, 2, 7, 7, 8, 5, 2, 7 Mean: Median: Thx hurry pls no explanation needed
Answers
Answer:
mean is 5
median is (5+5)/2 = 5
Step-by-step explanation:
Answer:
median is 5
mean is 5
Step-by-step explanation:
consider the system of linear equations
consider the system of linear equations
6x+2y – z=4
X +5y+z=3
2x+y+4z=27
A, solve the system by
I. Gassian elimination method,
II. LU- decomposition method
III. Gauss- Jacobi method,and
IV. Gauss-seidel method,
Answers
I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.
II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.
III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.
IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.
I. Gaussian Elimination Method:
To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:
| 6 2 -1 | 4 |
| 1 5 1 | 3 |
| 2 1 4 |27 |
We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.
After performing the necessary row operations, we obtain the following reduced row-echelon form:
| 6 2 -1 | 4 |
| 0 4 2 | -1 |
| 0 0 3 | 6 |
From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.
II. LU-Decomposition Method:
LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.
III. Gauss-Jacobi Method:
The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.
IV. Gauss-Seidel Method:
Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.
Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.
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Help please!
Select the correct answer.
Answers
j < –0.65 The variable in the inequality is .
Answers
Answer:
NO SE PERO LOS AMO A TODOS CHIKISTRIKIS
Step-by-step explanation:
SORRY NO SPEAK ENGLISH
Zoie is painting a picture that is 15 by 27 inches. She plans to frame it in a frame x inches wide.
1) Write a polynomial that will be the area of the framed picture.
2) What will be the area of the picture with the frame if x=3?
Answers
The polynomial area of the framed picture is (27 + 2x) * (15 + 2x) and the value is 693 square units
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the area of the framed picture?The given parameters are
Width = 15
Length = 27
Also, we have
Length of the frame = x
This means that the area of the framed picture is
Area = (Length + 2 * Length of the frame) * (Width + 2 * Length of the frame)
Substitute the known values in the above equation
Area = (27 + 2x) * (15 + 2x)
The value of the area when x = 3In (a), we have
Area = (27 + 2x) * (15 + 2x)
When x = 3, we have
Area = (27 + 2 x 3) * (15 + 2 x 3)
Evaluate
Area = 693
Hence, the area is 693 square units
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Six Pepperidge Farm bagels were weighed, yielding the following data (grams):
117.6
109.5
111.6
109.2
119.1
110.8
(Note: 4 ounces = 113.4 grams)
a. Assuming that the six bagels are a random sample and the weight is normally distributed, estimate the true average weight and standard deviation of the weight using maximum likelihood.
b. Again assuming a normal distribution, estimate the weight below which 95% of all bagels will have their weights. (Hint: What is the 95th percentile in terms of μ and σ? Now use the invariance principle.)
Answers
Answer:
A) Average weight = 112.97
standard deviation = 3.913
B) 119.4069
Step-by-step explanation:
A) Estimate the true average weight and standard deviation of the weight
attached below is a detailed solution
Average weight = 112.97
standard deviation = 3.913
B) Assuming a normal distribution Estimate the weight below
attached below is a detailed solution
= 119.4069
A rectangle has a length 3x + 1 of and a width of Write an expression for the 3-9
perimeter of the rectangle.
Answers
The expression for the perimeter is P = 12x - 16
How to write an expression for the perimeter?The given parameters are
Length = 3x + 1
Width = 3x - 9
The perimeter is calculated as
P = 2 * (Width + Length)
So, we have
P = 2 * (3x + 1 + 3x - 9)
Evaluate
P = 2* (6x - 8)
Expand
P = 12x - 16
Hence, the expression for the perimeter is P = 12x - 16
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A circle has a diameter of 24 in what is the circumference pi is 3.14
Answers
Answer:
The circumference of a circle is calculated using the formula: C = πd, where C represents the circumference and d represents the diameter of the circle.
In this case, the diameter of the circle is given as 24 inches.
Using the formula, we can substitute the values:
C = πd
C = 3.14 * 24
C ≈ 75.36 inches
Therefore, the circumference of a circle with a diameter of 24 inches (and using π = 3.14) is approximately 75.36 inches.
Step-by-step explanation:
14. In a pattern that starts with 5, the next
number is 4 less than twice the previous
number. What is the 4th number in the
pattern?
E. 16
F. 8
G. 12
H. 20
Answers
Answer:
the answer would be G.12
Step-by-step explanation:
what is the correct answer?
Answers
Answer:
5
Step-by-step explanation:
Answer:4.5
[um i cant relay see it but il do my best]
3. Which of the following terms could not be used to describe the polygon below? A. quadrilateral B. square parallelogram D. rhombus
Answers
Factor 45u+ 72.
Write your answer as a product with a whole number greater than 1.
Answers
Answer:
9(5u+8)
Step-by-step explanation:
Please mark me as Brainliest if you're satisfied with the answer.
Tommy buys a new stereo that sells for $1052.75 plus taxes. At the time of the
purchase the taxes and a $40 deferral charge are paid. The selling price is paid in
12 monthly payments.
A) What is the total amount to be paid at the time of the purchase?
B) What is the amount of each monthly payment?
Answers
Answer: See explanation
Step-by-step explanation:
A. What is the total amount to be paid at the time of the purchase?
This will be the selling price of the stereo with the tax and the deferral. This will be:
= $1052.75 + $40
= $1092.75
B) What is the amount of each monthly payment?
Each monthly payment will be gotten by dividing the total payment to be made by 12. This will be:
= $1092.75 / 12
= $91.06
Find the value of x that makes AABC~ADEF.
B
8
12
光
A x+7 C
X =
D
24
E
48
3(x+3)
F
Answers
Answer:e
Step-by-step explanation:t
Which of the following are factor pairs for 54?select all that apply.
Answers
Answer:
The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.
Step-by-step explanation:
hope this helped:)
brainliest for the brains........................
The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.
Here, we have,
The factors of 54 are the numbers, that can divide 54 completely or evenly. When a pair of factors are multiplied together to produce the 54, then they are said to be pair factors. The factors divide the number completely. Hence, these factors cannot be a fraction.
Factors of 54: 1,2,3,6,9,18,27 and 54
Factor pairs of the number 54 are the whole numbers which are not a fraction or decimal number.
To find the factors of a number, 54, we will use the factorization method.
To find factors of 54, we have to divide 54 by all natural numbers from 1 to 54.
54 ÷ 1 = 54
54 ÷ 2 = 27
54 ÷ 3 = 18
54 ÷ 6 = 9
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you have a goal to sell 100 tickets to a school pizza party if you only completed 50 percent of your goal , did you sell more or fewer than 100 tickets ?
Answers
Answer:
you sold fewer than 100 tickets. you only sold 50 tickets out of your 100 ticket goal.
shape J is reflected in the line y=x and then translated. The result is shape K. a) what is the vector that describes the translation? b) if shape J was first translated and then reflected in the line y=x to give shape K, what would the vector be that describes that translation?
Answers
Using transformations, the vector that describes the translation that J underwent is:
(x,y) -> (x - 1, y + 2).
Which rules model these transformations?The vertices of the transformed figure K are given as follows:
(4,0), (6,0), (6,-1), (5,-1), (5,-2), (4,-2).
The rule for a reflection about the line y = x is given by:
(x,y) -> (y,x).
Hence, taking the vertices of figure K, the vertices of the translated figure were given by:
(0,4), (0,6), (-1,6), (-1,5), (-2,5), (-2,4).
The vertices of the original figure J are given as follows:
(1,2), (1,4), (0,4), (0,3), (-1,3), (-1,3).
Hence the vector rule from J to the translated figure is given as follows:
(x,y) -> (x - 1, y + 2).
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What is the y-intercept of the line with the equation y = 4 x + 2? a. -2 b. 4 c. 2 d. Negative one-half
Answers
Answer:
the correct answer is c
PLZ HELP FAST!!! WILL MARK THE BRAINLIEST -Which of the following is an equivalent form of the compound inequality −33 > −3x − 6 ≥ −6?
A) −3x − 6 > −33 and −3x − 6 ≥ −6
B)−3x − 6 < −33 and −3x − 6 ≥ −6
C) −3x > −33 and −6 ≥ −6
D)−3x − 6 < −33 and −3x − 6 ≤ −6
Answers
Answer:
B
Step-by-step explanation:
Its the same
Rewrite the function by completing the square. f(x)= x^2 +8x+4
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given the function
\(f\left(x\right)=\:x^2\:+8x+4\)
Let's rewrite the function by completing the square.
\(0=x^2+8x+4\)
Subtract 4 from both sides
\(x^2+8x+4-4=0-4\)
Simplify
\(x^2+8x=-4\)
Rewrite in the form (x+a)²=b
\(x^2+8x=-4\)
Rewrite in the form x²+2ax+a²
solve for a, 2ax = 8x
\(2ax=8x\)
Divide both sides by 2x
\(\frac{2ax}{2x}=\frac{8x}{2x}\)
simplify
\(a = 4\)
Add a²=4² to both sides
\(x^2+8x+4^2=-4+4^2\)
\(x^2+8x+4^2=12\)
Apply perfect square formula
(a+b)²= a²+2ab+b²
\(\left(x+4\right)^2=12\) ∵ \(x^2+8x+4^2=\left(x+4\right)^2\)
Thus,
\(\left(x+4\right)^2=12\)
what is the aswer to 5 is 2 more than?
Answers
Answer:
Cuz 5 is greater than 2
Step-by-step explanation:
Answer:
3
Step-by-step explanation: