Question

In Exploration 2.4.1 you were asked to find the inverse of a matrix.

[ 1 -1 2 | 1 0 0 ]
Now consider this matrix [ 2 0 3 | 0 1 0 ] Select two steps that result
[ 0 1 -1 | 0 0 1 ]
[ 1 -1 2 | 1 0 0 ]
In the following matrix : [ 0 1 0 | -2 1 -1 ]
[ 0 1 -1 | 0 0 1 ]
A) Step 1: R2 → R2-2
Step 2: Rs → R3
B) Step 1: R2 → R2-2R3
Step 2: R2 → R2-R1
C) Step 1: R3 → R-2R1
Step 2: Rs → R3-R2
D) Step 1: R2 → R2-2R1
Step 2: R2 → R₂- Rs
E) Step 1: R2 → R₂- R
Step 2: R2 → R₂- R1

Answer 1

To obtain the matrix [0 1 -1 | 0 0 1] from the given matrix [2 0 3 | 0 1 0], we need to perform row operations. Step 1: R2 → R2 - R1. Step 2: R2 → R2 - R3.

Step-by-step explanation:

To obtain the matrix [0 1 -1 | 0 0 1] from the given matrix [2 0 3 | 0 1 0], we need to perform row operations.

Step 1: R2 → R2 - R1

This step subtracts the first row from the second row.

[2 0 3 | 0 1 0] - [1 -1 2 | 1 0 0] = [1 1 1 | -1 1 0]

Step 2: R2 → R2 - R3

This step subtracts the third row from the second row.

[1 1 1 | -1 1 0] - [0 1 -1 | 0 0 1] = [1 0 2 | -1 1 -1]