Question

Solve the following system of equations by row reduction and show that the answer is

( -1, -4,5)

x-2y+3z= 22
2x+3y-z=5
3x+y-5z= 32

Answer 1

To solve the system of linear equations by row reduction, you start by converting the equations to augmented matrix form and then perform row operations to reach row-echelon form. From there, you can find the solution, which should be (-1, -4, 5), by back-substitution.

Step-by-step explanation:

To solve the system of equations by row reduction, we’ll use the equations given:

1. x - 2y + 3z = 22
2. 2x + 3y - z = 5
3. 3x + y - 5z = 32

First, we’ll write the equations in augmented matrix form.

[1 -2 3 | 22]

[2 3 -1 | 5]

[3 1 -5 | 32]

Next, we apply row operations to reduce the matrix to row-echelon form:

• Use R2 - 2R1 -> R2
• Use R3 - 3R1 -> R3
• Continue with row operations until you reach row-echelon form.

After the row reduction, you should get a triangular matrix that allows you to use back-substitution to find the values of x, y, and z. If done correctly, you should find that the solution to the system is indeed (-1, -4, 5).