Elementary row operations- Linear Algebra

[lina29]

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?

 

[Snoogx]

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

 

[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?

 

[Ray Vickson]

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

 

[Snoogx]

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

RGV

what he said.