# Homework Help: Elementary row operations- Linear Algebra

1. Sep 16, 2011

### lina29

1. The problem statement, all variables and given/known data

Consider the following 3 row operations performed to a 4x3 matrix A used to transform it into matrix B:
E1: -4R1+R4-> R4
E2: R2<->R3
E3: (1/2)R4-> R4
From there I am asked to find E1, E2, E3.

3. The attempt at a solution

I assumed the identity matrix I would start out with was
1 0 0
0 1 0
0 0 1
0 0 0

and then by using E1 the matrix would become
1 0 0
0 1 0
0 0 1
-4 0 0

However, the answer was counted wrong. Am I approaching the question the wrong way or am I using the wrong identity matrix?

2. Sep 16, 2011

### Snoogx

The identity matrix is actually 4x4:
[1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1]

3. Sep 16, 2011

### lina29

ohh thank you so much! I got the correct answers but why is the identity matrix a 4x4 when the original matrix is a 4x3?

Last edited: Sep 16, 2011
4. Sep 16, 2011

### Ray Vickson

Because you perform row operations on an mxn matrix by multiplying on the left by an mxm matrix.

RGV

5. Sep 16, 2011

### Snoogx

what he said.