Question

Find the elementary matrix E such that EA = B for A and B given below.

A =
[6 4 4]
[-2 -2 -2]
[4 4 -4]

B=
[-14 -16 24]
[-2 -2 -6]
[4 4 -4]

Answer 1

To find the elementary matrix E such that EA = B, we can use the formula E = BA^-1. First, find the inverse of matrix A, then multiply B by the inverse of A to get the elementary matrix E.

Step-by-step explanation:

To find the elementary matrix E such that EA = B for the given matrices A and B, we can use the formula E = BA-1. First, we need to find the inverse of matrix A. Then, we can multiply B by the inverse of A to get the elementary matrix E.

Step 1: Find the inverse of matrix A:
A-1 = inverse of A =

[1/16 -3/16 -1/16]
[1/8 -1/8 -1/8]
[1/4 -1/4 -1/4]

Step 2: Multiply B by A-1 to get the elementary matrix E:
E = B * A-1 =

[5/2 5/2 -1/2]
[5/4 3/4 1/4]
[-5/4 -3/4 -1/4]

Therefore, the elementary matrix E such that EA = B is:
E =

[5/2 5/2 -1/2]
[5/4 3/4 1/4]
[-5/4 -3/4 -1/4]