Answer:
x1 = -36, x2 = -32, and x3 = 7
Explanation:
not 100% sure I understand the question but here's my best guess
To solve the system of equations, we can use the method of matrices and Gaussian elimination. Let's represent the system of equations in matrix form as: [A] [X] = [B],where:
[A] is the coefficient matrix,
[X] is the column matrix of variables (x1, x2, x3),
[B] is the column matrix of constants (3, -8, 10).
The coefficient matrix [A] is:| 1 -1 1 |
| -2 3 1 |
| 4 -2 10 |The variable matrix [X] is:| x1 |
| x2 |
| x3 |The constant matrix [B] is:| 3 |
| -8 |
| 10 |Now, we will use Gaussian elimination to solve the system of equations:Step 1: Perform row operations to get a leading 1 in the first row and zeros below it.R1 -> R1 + R2,
R1 -> R1 - 4R3.The new matrix is:| 1 -1 1 | | x1 | | 3 |
| 0 1 3 | | x2 | | -11 |
| 0 2 6 | | x3 | = | -2 |Step 2: Now, make the second element in the second row (R2,2) as 1.R2 -> R2 - 2R3.The new matrix is:| 1 -1 1 | | x1 | | 3 |
| 0 1 3 | | x2 | | -11 |
| 0 0 0 | | x3 | = | 7 |Step 3: The system has a row of zeros, which means it is an underdetermined system with infinite solutions. Let's express x3 in terms of x1 and x2:x3 = 7.Step 4: Substitute x3 = 7 into the second row to find x2:x2 + 3(7) = -11,
x2 = -11 - 21,
x2 = -32.Step 5: Substitute x2 = -32 and x3 = 7 into the first row to find x1:x1 - (-32) + 7 = 3,
x1 + 32 + 7 = 3,
x1 + 39 = 3,
x1 = 3 - 39,
x1 = -36.
So, the solution to the system of equations is
x1 = -36, x2 = -32, and x3 = 7.