Explain how to find coordinates for Q

The matrix of the linear transformation t : R4 → R3 defined by t(x1, x2, x3, x4) = (2x1 3x2 x4, 5x1 9x3 − x4, 4x1 2x2 − x3 7x4) is:

| 2 0 0 0 |

| 0 0 5 -1 |

| 4 8 -2 7 |

To determine the matrix of the linear transformation t : R4 → R3, we need to find the image of the standard basis vectors under the transformation t. The standard basis vectors of R4 are e1 = (1, 0, 0, 0), e2 = (0, 1, 0, 0), e3 = (0, 0, 1, 0), and e4 = (0, 0, 0, 1).

Applying the transformation t to each of these vectors, we get:

t(e1) = (2, 0, 4)

t(e2) = (0, 0, 8)

t(e3) = (0, 5, -2)

t(e4) = (0, -1, 7)

Thus, the matrix of the linear transformation t with respect to the standard bases of R4 and R3 is:

| 2 0 0 0 |

| 0 0 5 -1 |

| 4 8 -2 7 |

Each column of this matrix represents the image of the corresponding basis vector of R4, expressed as a linear combination of the basis vectors of R3.

Note that the matrix has 3 rows and 4 columns, reflecting the fact that the transformation maps R4 to R3.

The first column represents the image of the first basis vector e1, which is (2, 0, 4) in R3.

Similarly, the second, third, and fourth columns represent the images of the basis vectors e2, e3, and e4, respectively.

Therefore, the matrix of the linear transformation t : R4 → R3 defined by t(x1, x2, x3, x4) = (2x1 3x2 x4, 5x1 9x3 − x4, 4x1 2x2 − x3 7x4) is:

| 2 0 0 0 |

| 0 0 5 -1 |

| 4 8 -2 7 |

For more such question on matrix

https://brainly.com/question/2456804

#SPJ11

Answer:

neither

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

All rational numbers can be written as fractions.

From the Bayes' theorem, the proportion of probability of adults for which the test would be positive is equals to the 0.02097.

The Bayes' theorem, generally defines as the Bayes' rule, is a mathematical formula used in statistics and probability theory. We have a data of adults having a rare disease about the a diagnostic test. Let us consider two events defined as

A : person or adult has disease

B : test indicate person or adult has disease

Probability that a selected adult has a rare disease for which a diagnostic test developed, P(A) = 0.001

Probability the test will be positive (a person with the disease, P( B|A ) = 0.99

Probability the test will be positive( a person without the disease), P( B|A')

= 0.02

We have to determine the probability or proportion adults for which the test would be positive, i.e., P(B). Using the conditional probability theorem, \(P(B|A) = \frac{ (A ∩B) }{P(A)} = P(A|B)\frac{P(B)}{P(A} \)

P(B) = P( B∩A) + P(B ∩ A')

= P( B|A)P(A) + P( B|A')P(A')

\(P(A') = 1 - P(A) = 1 - 0.001 = 0.999 \)

substitute all known values in above formula,

=> P(B) = 0.99 × 0.001 + 0.02× 0.999

= 0.00099 + 0.01998

= 0.02097

Hence, required value is 0.02097.

For more information about Bayes'theorem, visit :

https://brainly.com/question/14989160

#SPJ4

Answer: 16

Step-by-step explanation:

The volume is 1088.64 cm^2 of a rectangular prism with 7.2cm,8.4cm,18cm.

What is volume?

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

a rectangular prism with 7.2cm,8.4cm,18cm

we know,

the volume is

V= l.b.w

here,

l= 7.2 cm

b= 8.4 cm

w= 18cm

i.e. V= 1088.64 cm^2

Hence, The volume is 1088.64 cm^2 of a rectangular prism with 7.2cm,8.4cm,18cm.

To learn more on volume click :

brainly.com/question/1578538

#SPJ1

Answer: for the question 2 I gave you the step by step explanation in the picture so you can probably better understand where you did wrong , I hope it will be helpful for you, have a nice rest of your day:)

Answer:

see explanation

Step-by-step explanation:

(f + g)(x)

= f(x + g(x)

= x² + 1 + 5 - x ← collect like terms

= x² - x + 6

--------------------------------

(f - g)(x)

=f(x) - g(x)

= x² + 1 - (5 - x)

= x² + 1 - 5 + x ← collect like terms

= x² + x - 4

Answer:

instead of the 4, you can put the 80 and do the 20x4?

Step-by-step explanation:

i dont know if you can do that for whatever ur doing, just a suggestion

I lost my train of thought, but i was thinking of something like that

The expected number of dollars you will win or lose playing this game once is -$0.50. To calculate the expected value, we multiply each outcome by its probability and sum them up.

In the first round, the probability of rolling a 1 is 1/6, and the corresponding outcome is $1.

Expected value for the first round = (1/6) * $1 = $1/6.

In the second round, the probability of rolling a 2 is 1/6, and the corresponding outcome is $2.

Expected value for the second round = (1/6) * $2 = $2/6 = $1/3.

In the third round, the probability of rolling a 3 is 1/6, and the corresponding outcome is $3.

Expected value for the third round = (1/6) * $3 = $3/6 = $1/2.

If you lose all three rounds, the outcome is -$3 with a probability of (5/6) * (5/6) * (5/6) = 125/216.

The expected value for losing all three rounds = (125/216) * (-$3) = -$125/72.

Now, we sum up the expected values for each round and the outcome of losing all three rounds:

Expected value = ($1/6) + ($1/3) + ($1/2) + (-$125/72)

             = $12/72 + $24/72 + $36/72 - $125/72

             = ($12 + $24 + $36 - $125)/72

             = -$53/72

             ≈ -$0.50.

Therefore, the expected number of dollars you will win or lose playing this game once is -$0.50.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Answer: 2/15

Step-by-step explanation: First multiply the numerators together and then denominators together.

Numerators= 2 and 1

(numerators) 2 x 1 = 2

Denominators= 3 and 5

(denominators) 3 x 5 = 15

Hence, you get 2/15

In scientific notation, a number is written as the base number times ten raised to a power. The base number, known as the significand, is also referred to as the mantissa.

The term mantissa is used for the fractional part of a common logarithm as well.

The mantissa is the fractional part of a logarithm. In the context of scientific notation, the mantissa refers to the base number, which is multiplied by 10 raised to a certain power to represent a number.

In other words, the mantissa is the significant digits of a number, excluding the leading and trailing zeros, expressed as a decimal fraction between 1 and 10. For example, in the number 3.24 x 10^5, the mantissa is 3.24.

Learn more about mantissa,

https://brainly.com/question/30708908

#SPJ11

Answer:

His original farm was 333 1/3 acres

He has 66 2/3 acres of his land left

Step-by-step explanation:

Lex

His total farmland = x

1/2 of x = Mr frost

100 acres = Mr slate

Remaining = 1/5x

His total farmland = Mr Frost + Mr slate + remaining farmland

x = 1/2x + 100 + 1/5x

x = 5x+2x/10 + 100

x = 7/10x + 100

x - 7/10x = 100

10x-7x/10 =100

3/10x = 100

Divide both sides by 3/10

x = 100 ÷ 3/10

= 100 × 10/3

= 1,000/3

= 333 1/3 acres

His original farm was 333 1/3 acres

He has 1/5 of his original farm

1/5 × 1000/3

= 1,000 / 15

= 66 10/15

= 66 2/3 acres

He has 66 2/3 acres of his land left

ANSWER

EXPLANATION

The given translation

This means the shape will be translated 3units to the right and 2 units up.

That is;

Answer:

243 .....................

Answer:

He can read 80 in four hours.

To carpet the rectangular floor, it will cost $1,137.6. The result if obtained by multiplying the area of the carpet by the cost per square yard.

To calculate the cost of a product, multiply the product price for one item by the quantity.

We have a rectangular floor with a dimension of 27 feet by 24 feet. The carpet cost is $15.8 per square yard. Find the total cost to carpet it!

Let's change the unit of length.

The area of the carpet is

A = 9 yard × 8 yard

A = 72 square yard

The total cost is

C = A × price/square yard

C = 72 × $15.8

C = $1,137.6

Hence, the total cost to carpet the floor is $1,137.6.

Learn more about total cost of a product here:

brainly.com/question/29061014

#SPJ4

Answer:

\(i\sqrt4 ~ \text{and} ~ 2i\)

Step-by-step explanation:

\(\sqrt{-4}\\\\=\sqrt{-1} \sqrt4\\\\=i\sqrt4\\\\=2i\)

Answer:

5 hours

Step-by-step explanation: in 5 hours 60 degrees would become 50 degrees and so wold the 35 degrees.

The expression that signifies Katherine’s final cost F= P + T= $466

The number of pansies to be arranged around each tree = 15 pansies

The cost of pansies(P) = 15 × 8 × 2.50 = $300

The number of juniper trees available = 8

The cost of the trees available(T) = 8 × 20.75= $166

Therefore Katherine's final cost(F)= $300 + $166 = $466

The expression to find Katherine’s final cost = F= P + T

Learn more about addition here:

https://brainly.com/question/24536701

#SPJ1

Answer:

-24

Step-by-step explanation:

First find f(3), which is the value of the blue line when x =3

f(3) = -2

Then find g(-1) which is the value of the red line when x= -1

g(-1) = 6

-6 f(3) - 6*g(-1)

-6*-2 - 6(6)

12 - 36

-24

MATHEMATICALLY WE WRITE THIS AS

\( = \frac{1}{2} (17 + 9) \\ = \frac{1}{2} (26) \\ = 13\)

THE ANSWER IS 13

GOODLUCK

Answer:8

-11+19 (absolute value)

Add the opposite

19-11=8

Keep the sign of the greater absolute value in this case the greater value is ninteen but it can be the negitive.

So your answer is eight (8)

Step-by-step explanation: see above

Answer:

x=−3 or x=5

so yeah

Answer:

solve for x

Step-by-step explanation:

i hope this helps

The present age of the Bernard is, 23.

What is age?

Given a date of birth, this free age calculator calculates age in terms of years, months, weeks, days, hours, minutes, and seconds.

Calculated using the population's arithmetic mean, average age. The median age is a factor that determines the population's average age.

As given, in 7 years Bernard will be twice as old as he was 8 years ago.

Let  the present age of Bernard = x

Bernard age after 7 years = x + 7.

Bernard age before 8 years = x - 8.

From the given information,

2(x - 8) = x + 7

2x - 16 = x + 7

2x - x = 16 + 7

x = 23

Therefore, the present age of Bernard is 23.

To know more about the age, click on the link

https://brainly.com/question/343671

#SPJ1

The answer is 30 laps. Don’t  worry about anything else except for the laps and hours. Each hour have 60 minute so you just divide 1800 with 60 and get 30.

Answer:

You can buy 10 bulbs of elephant garlic

Step-by-step explanation:

Since each bulb of elephant garlic is 2.

1 x 2 = $2

That is the cost of 1 elephant garlic.

10 x 2 = $20

That is the cost of 10 elephant garlic.

Firstly, we will need to try the following options one after the other in order to ascertain our answer

The first option

To find the distance between two points

Distance = Higher number - Lower number

-3 - 20

= - 23

This is very wrong because it has a negative sign

The second option

7 - (-16)

In mathematics, - x - = +

7 + 16

7 + 16 = 23

The answer is OPTION B

Answer:

Step-by-step explanation:

The initial height is the beginning of the graph, or in this case, x=0. So the initial height is 1.5.