Question

Which of the following matrices could be used to solve the system of equations?

3x +2y+z= -5
4x=4
2x + 2y + 2z = 10
a) [3, 2, 1; 4, 0, 0; 2, 2, 2]
b) [4, 2, 1; 4, 4, 0; 2, 2, 2]
c) [3, 0, 1; 4, 4, 0; 2, 2, 2]
d) [3, 2, 1; 1, 0, 0; 2, 2, 2]

Answer 1

The matrix that could be used to solve the system of equations is option (c) [3, 0, 1; 4, 4, 0; 2, 2, 2].

Step-by-step explanation:

The matrix that could be used to solve the system of equations is option (c) [3, 0, 1; 4, 4, 0; 2, 2, 2].

To determine this, we need to look for the matrix that has the coefficients of x, y, and z in the correct positions. The system of equations can be written in matrix form as:

[3, 2, 1; 4, 0, 0; 2, 2, 2] * [x; y; z] = [-5; 4; 10]

By comparing this matrix equation to the given options, we can see that option (c) matches the coefficients of x, y, and z in the first row and the constants in the right-hand side of the equation.