Answer:

Step-by-step explanation:

To equate the corresponding elements of two matrices, we can set up a system of equations. In this case, we can equate the elements of the two matrices:

For the first row:
x + 3 = 0
2y + x = -7

For the second row:
z - 1 = 3
4a - z = 2a

Solve each set of equations separately to find the values of x, y, z, and a:

**First Row Equations:**
From the first equation, we get: x = -3.
Substitute x = -3 into the second equation: 2y - 3 = -7
Solve for y: 2y = -4, y = -2.

**Second Row Equations:**
From the third equation, we get: z = 4.
Substitute z = 4 into the fourth equation: 4a - 4 = 2a
Solve for a: 2a = 4, a = 2.

Now that we have the values of x, y, and z, we can find their sum:
x + y + z = -3 + (-2) + 4 = -1.

Therefore, the value of x + y + z is -1.

To equate two matrices, their corresponding elements should be equal. Let's compare the elements of the two matrices:

Given Matrix:

[a11 = x+3]   [a12 = 2y+x]

[a21 = z-1]   [a22 = 4a-z]

Desired Matrix:

[a11 = 0]   [a12 = -7]

[a21 = 3]   [a22 = 2a]

Comparing the elements:

1. For a11: x + 3 = 0  =>  x = -3

2. For a12: 2y + x = -7  =>  2y - 3 = -7  =>  2y = -4  =>  y = -2

3. For a21: z - 1 = 3  =>  z = 4

4. For a22: 4a - z = 2a  =>  4a - 4 = 2a  =>  2a = 4  =>  a = 2

Now that we have x, y, and z values:

x = -3

y = -2

z = 4

We can calculate the sum:

x + y + z = -3 + (-2) + 4 = -1

So, x + y + z = -1.