pply elementary operations of linear system, solve the following system of linear equations.State your steps clearly. (hint: please use Gaussian elimination when conducting row opera-tions)(a)2x1 + 3x2 = 24x1 − 5x2 = 15(b)x1 + x2 − x3 = 62x1 + 4x2 + 5x3 = 113x1 + 4x2 + 10x3 = 8

Sure, let's solve these systems of equations using Gaussian elimination.

(a) We have the system of equations:

2x1 + 3x2 = 24 4x1 - 5x2 = 15

Step 1: Write the system of equations in matrix form. We get:

[2, 3 | 24] [4, -5 | 15]

Step 2: We can simplify this system by subtracting 2 times the first row from the second row. This gives us:

[2, 3 | 24] [0, -11 | -33]

Step 3: Now, we can divide the second row by -11 to make the coefficient of x2 equal to 1. We get:

[2, 3 | 24] [0, 1 | 3]

Step 4: Finally, we can subtract 3 times the second row from the first row to eliminate x2 from the first equation. We get:

[2, 0 | 18] [0, 1 | 3]

So, the solutions are x1 = 9 and x2 = 3.

(b) We have the system of equations:

x1 + x2 - x3 = 6 2x1 + 4x2 + 5x3 = 11 3x1 + 4x2 + 10x3 = 8

Step 1: Write the system of equations in matrix form. We get:

[1, 1, -1 | 6] [2, 4, 5 | 11] [3, 4, 10 | 8]

Step 2: Subtract 2 times the first row from the second row and 3 times the first row from the third row. We get:

[1, 1, -1 | 6] [0, 2, 7 | -1] [0, 1, 13 | -10]

Step 3: Subtract the third row from the second row. We get:

[1, 1, -1 | 6] [0, 1, -6 | 9] [0, 1, 13 | -10]

Step 4: Subtract the second row from the third row. We get:

[1, 1, -1 | 6] [0, 1, -6 | 9] [0, 0, 19 | -19]

Step 5: Divide the third row by 19. We get:

[1, 1, -1 | 6] [0, 1, -6 | 9] [0, 0, 1 | -1]

Step 6: Add the third row to the first row and add 6 times the third row to the second row. We get:

[1, 1, 0 | 5] [0, 1, 0 | -3] [0, 0, 1 | -1]

Step 7: Subtract the second row from the first row. We get:

[1, 0, 0 | 8] [0, 1, 0 | -3] [0, 0, 1 | -1]

So, the solutions are x1 = 8, x2 = -3, and x3 = -1.