# Linear Algebra- Matrices

## Homework Statement

You are given matrices A:

A=
[-4 5 9 0 3
-5 1 3 8 -5
-6 0 4 0 -9
-1 -1 -4 3 -5]
and

B=
[-4 5 9 0 3
-6 0 4 0 -9
-40 8 24 64 -40
-1 -1 -4 3 -5 ]

Find two elementary matrices E and F that transform matrix A into matrix B.

## Homework Equations

The solution might not be unique, however, after multiplying A on the left with elementary matrices E and F your result should be matrix B. That is, F E A = B.

## The Attempt at a Solution

I know one Elementary matrix already which is R2*8
and the second elementary matrix swaps row 2 with row 3

do I write it like this:
F=
[1 0 0 0 0
0 8 0 0 0
0 0 1 0 0
0 0 0 1 0] --is it okay to have the last column full of zeros??

and the next elementary matrix, do i write it like this:
[1 0 0 0 0
0 0 1 0 0
0 1 0 0 0
0 0 0 1 0]

Last edited:

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I think elementary matrices need to be square matrices ...

edit 2: (undoing edit 1 lol): can you multiply those matrices?!
5x4 * 5x4..

Last edited:
Defennder
Homework Helper
Note that elementary matrices are invertible, so they have to be square matrices. Note that a 4x4 matrix multiplied to a 4x5 matrix will give you a 4x5 matrix, which is what you want.

As you pointed out, you need 2 matrices, one which reflects 8*R2 and one which swaps R2, R3. Note that the elementary matrix which performs a desired row operation when multiplied to another matrix is obtained by executing the same row operation on the identity matrix.

HallsofIvy