# Elementary row operations- Linear Algebra

## Homework Statement

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.

## 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?

## Answers and Replies

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

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:
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
ohh thank you so much! I got the correct answers no but why is the identity matrix a 4x4 when the original matrix is a 4x3?

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

RGV

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

RGV

what he said.