Final answer:
To set up the matrix for the given system of linear equations, you create a coefficient matrix with the coefficients of the variables x, y, and z, and a constant matrix with the constants from the right-hand side of the equations. The coefficient matrix is [-5 4 -1; 3 -3 -5; -2 -5 4], and the constant matrix is [11; 17; 0].
Step-by-step explanation:
To set up the matrix for the system of equations:
- -5x + 4y - z = 11,
- 3x - 3y - 5z = 17,
- -2x - 5y + 4z = 0,
We create the coefficient matrix from the left-hand side of the equations and the constant matrix from the right-hand side. The coefficient matrix contains the coefficients of the variables x, y, and z, while the constant matrix contains the constants 11, 17, and 0.
The coefficient matrix is:
[-5 4 -1]
[ 3 -3 -5]
[-2 -5 4]
And the constant matrix or column vector is:
[11]
[17]
[ 0]
This is the standard form for representing a system of linear equations as a matrix equation.