106k views
5 votes
Find a solution to the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations 4x-2y-5z=-51 4x-y-2z=-36

User SteveP
by
7.9k points

1 Answer

2 votes

Final answer:

To find a solution to the system of equations, we need to find the reduced row-echelon form of the augmented matrix. After performing row operations, we can read off the values of x, y, and z from the reduced matrix.

Step-by-step explanation:

To find a solution to the system of equations, we need to find the reduced row-echelon form of the augmented matrix for the system.

The augmented matrix for the system of equations is:

[4 -2 -5 -51; 4 -1 -2 -36]

Using row operations, we can perform the following steps to reduce the matrix to its reduced row-echelon form:

Step 1: Divide row 1 by 4: [1 -0.5 -1.25 -12.75; 4 -1 -2 -36]

Step 2: Replace row 2 with row 2 - 4(row 1): [1 -0.5 -1.25 -12.75; 0 1 1 3]

Step 3: Divide row 2 by 1: [1 -0.5 -1.25 -12.75; 0 1 1 3]

This gives us the reduced row-echelon form of the augmented matrix. To find the solution to the system of equations, we can read off the values of x, y, and z from the matrix.

x = -12.75, y = 3, z = 0

User Toufik
by
7.8k points