What is the value of a?

Enter your answer in the box. Enter your answer as a simplified fraction.

==========================================

Work Shown:

The scalar (2/5a+6) multiplies with the matrix on the left side to get the matrix on the right side

So this is what your steps could look like

[tex](\frac{2}{5}a+6)\begin{bmatrix}3 \\ -2 \\ 7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\\begin{bmatrix}(\frac{2}{5}a+6)*3 \\ (\frac{2}{5}a+6)*(-2) \\ (\frac{2}{5}a+6)*7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\[/tex]

[tex]\begin{bmatrix}\frac{2}{5}a*3+6*3 \\ \frac{2}{5}a*(-2)+6*(-2) \\ \frac{2}{5}a*7+6*7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\\begin{bmatrix}\frac{6}{5}a+18 \\ -\frac{4}{5}a-12 \\ \frac{14}{5}a+42\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\[/tex]

The last matrix equation leads to this system of equations

[tex]\begin{cases}\frac{6}{5}a+18=15 \\ -\frac{4}{5}a-12=-10 \\ \frac{14}{5}a+42=35\end{cases}\\\\\\[/tex]

If we pick any of those equations, and solve for 'a', then we'll get our answer.

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

Let's say we pick the first equation

(6/5)a+18 = 15

(6/5)a = 15-18

(6/5)a = -3

a = -3(5/6)

a = -15/6

a = -5/2

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

If we pick on the second equation, then,

(-4/5)a-12 = -10

(-4/5)a = -10+12

(-4/5)a = 2

a = 2(-5/4)

a = -10/4

a = -5/2

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

Or we could solve the third equation for 'a'

(14/5)a+42 = 35

(14/5)a = 35-42

(14/5)a = -7

a = -7*(5/14)

a = -35/14

a = -5/2

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

You only need to solve one equation to find 'a', though it's good practice to solve all three to see all three rows agreeing with one another.

The multiplication of the matrix by a constant will multiply for each term in the matrix value of the "a" given system of the matrix will be -2.5.

A matrix is a collection of numbers lined up in rows and columns to produce a rectangular array.

In computer graphics, where they have been used to describe picture transformations and other alterations, matrices have vital applications as well in many sectors.

As per the given system of the matrix.

When we multiply anything in a matrix then it will multiply to each and every term of the matrix.

Therefore the (2/5)a + 6 will be multiplied by 3,-2, and 7 each.

So the first term of the left-hand side matrix becomes,[(2/5)a + 6]3

If we compare two matrices then each corresponding term will be the same.

Therefore, the first term of the left-hand matrix = first term of the right-hand matrix

[(2/5)a + 6]3 = 15

6a/5 + 18 = 15

6a/5 = -3

6a = -15

a = -15/6 = -2.5

Hence "The value of the "a" given system of the matrix will be -2.5".

For more about matrices,

brainly.com/question/11367104

#SPJ5

alice sold 3 more than 2 times the number of magazines Josh sold. Alice sold a total of 27 magazines. How many magazines does Josh sell?

Which statement can be concluded using the true statements?
If a quadrilateral has 4 equal sides and 4 equal angles, then it is a square.
If a figure is a square, then each of its angles must measure 90 degrees.
If a quadrilaterál has 4 equal sides and 4 equal angles, then each of its angles must measure 90 degrees.
If a quadrilateral has 4 equal sides and 4 equal angles, then none of its angles measures 90 degrees.
If all four angles in a quadriateral measure 90 degrees, the quadrilateral is a square.
If all four angles in a quadriateral measure 90 degrees, the quadrilateral cannot be a square.

What is the equation for a line with slope = 3 that passes through point (2, 5)?
a. y = 3x - 13
b. y = 3x - 1
C. y = 3x - 5

guys whats 1 + 1?
im rly confused plz help

Solve the equation

6=u/9+10

please help !!
12x + 14 = 6x + 7 (+) 9x - 5 find the value of x

A die is thrown. What is the probability of getting 6?
(a) 0
b 1/6
c 1/2
d 1​

Find the 125% of 600lb

The merry-go-round at the fair rotates 12 times each minute, and children are 15 feet from the center of the wheel when they are in their seats. What is the linear velocity of the children in feet per hour?
360π
720π
21,600π
43,200π

7.5 more than the quotient of h and 3 is w

(x+10)(3x+10) they are linear pair

A health psychologist knew that corporate executives in general have an average score of 2.55 with a standard deviation of 0.5 on a stress inventory and that the scores are normally distributed. In order to learn whether corporate executives who exercise regularly have different stress scores, the psychologist measured the stress of 30 exercising executives and found them to have a mean score of 2.76. a. Using the five steps of hypothesis testing, was the group of 30 exercising executives different from executives in general? (Use the .05 significance level.) Be sure to sketch the distributions involved. Be sure to fully state the five steps and show ALL calculations/work. b. Additionally, explain the logic of what you did to a person who understands hypothesis testing for studies in which the sample consists of a single individual but is unfamiliar with hypothesis testing involving a sample of more than one individual. (Be sure your explanation includes a discussion of the distribution of means--what it is, what it is made of, the concept of how it is created, how itʹs characteristics are created, its role in the overall hypothesis testing process.)

5/9 is rational or irrational

-12(23 – 17) - (-2) × 62​

PLEASE HELP NOWWW!!!!!! A country consists of two islands. The population of birds on one island is 1.105 million, and the population of birds on the other island is 2.21 million. Which expression finds the population of birds for this country?
1. 1.105 million + 2.021 million
2. 1.15 million + 2.21 million
3. 1.105 million + 2.201 million
4. 1.105 million + 2.210 million

PLZ HELP FAST!!!!!!!!​

purchased $2,300 worth of supplies on account. Prior to the purchase, the balance in the supplies account was $350. On December 31, the fiscal year-end for Unidevo, it is determined that $500 of supplies still remain. What is the balance in the supplies account after adjustment?

can someone help me it is math

Select all of the ratios that are equivalent to 8:6

To find the quotient Three-fourths divided by one-eighth, multiply Four-thirds by One-eighth. multiply Three-fourths by 8. multiply Four-thirds by 8. multiply Three-fourths by One-eighth.

What is the distance between point A and point B? Enter your answer in the box.

In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .75, the same as the overall proportion of complaints settled in 2008
a. Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of .
b. Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
c. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of .
d. Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?

pls help rn if possible

solve for n
-53 + n = -28

Drag a reason to each box to complete the proof

what is 1/11 divided by 4?(FRACTION FORM)

I need help with 20 please thank you.

juan reads 300 pages in 5 days and jose reads 150 in 3 days are these reading rates equivalent

The price of a stock decreased by 60 cents one week, decreased 10 cents the next week, and decreased another 20 cents the following week. What is the average change in the price of the stock over the three weeks?

Drink Amount
Juice 250 mL
Milk
400mL
Water 1,500 mL
What is the total amount of liquid, in liters, that Whitney drinks each day?