Question

As Tia solved the system of equations below, she transformed matrices at different steps during the process.

-a-b+2c=7
2a+b+c=2
-3a+2b+3c=7
She noted the following matrices.
I 1 1 0 | 0, 0 1 0 | -1, 0 0 1 | 3
II -1 -1 2 | 7, 2 1 1 | 2, -3 2 3| 7
III 1 1 -2 | -7, 0 1 -5 | -16, 0 0 22 | 66
IV 1 1 0| -1, 0 1 0 | -1, 0 0 1 | 3
In which order should the matrices be arranged when solving the system from start to finish?
A. I, IV, III, II
B. II, III, IV, I
C. II, IV, I, III
D. IV, II, III, I

Answer 1

The correct order of the transformation matrices when solving the system of equations using matrix operations is B. II, III, IV, I; starting with the initial augmented matrix and proceeding through the steps of Gauss-Jordan elimination.

Step-by-step explanation:

To solve the system of equations using matrix transformations, we need to understand the process of matrix row operations and how they apply to solving systems of linear equations. The first step is to create an augmented matrix from the system. Next, we perform row operations to reach reduced row echelon form or row echelon form, from which we can back-substitute to find the solution. The matrices provided by Tia appear to be different steps in this process.

Matrix II represents the initial augmented matrix obtained from the system of equations. Matrices I, III, and IV seem to be intermediate steps, with matrix IV being closest to the reduced row echelon form. The correct order of the matrices, if we follow the standard sequence of Gauss-Jordan elimination, should be from the augmented matrix to the reduced row echelon form.

Therefore, the correct order of the transformation matrices when solving the system from start to finish is B. II, III, IV, I.