Elementary row operations- Linear Algebra

Click For Summary

Homework Help Overview

The discussion revolves around the application of elementary row operations on a matrix in the context of linear algebra. The original poster presents a problem involving a 4x3 matrix and the transformation into another matrix through specified row operations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply row operations to an identity matrix they assumed to be 3x3, leading to confusion about the correct dimensions of the identity matrix needed for the operations on a 4x3 matrix. Some participants clarify that the identity matrix should be 4x4, prompting questions about why this is the case.

Discussion Status

Participants are engaged in clarifying the dimensionality of the identity matrix in relation to the matrix being transformed. There is acknowledgment of the original poster's misunderstanding, and some guidance has been provided regarding the necessity of using a 4x4 identity matrix for the row operations on a 4x3 matrix.

Contextual Notes

There is an ongoing exploration of the relationship between the dimensions of the identity matrix and the matrix undergoing transformation, as well as the implications of performing row operations on matrices of different sizes.

lina29
Messages
84
Reaction score
0

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?
 
Physics news on Phys.org
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:
lina29 said:
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
 
Ray Vickson said:
Because you perform row operations on an mxn matrix by multiplying on the left by an mxm matrix.

RGV

what he said.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K