(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given a matrix A. So I can reduce A to ref(A). Let's say in ref(A), the columns that contain leading ones are column 1, 3, and 5. True or false:

(a) Columns 1, 3, and 5 from ref(A) form the column space of ref(A).

(b) The corresponding column 1, 3, and 5 from the original matrix A form the column space of matrix A.

(c) Columns 1, 3, and 5 from ref(A) form the column space of the matrix A.

(d) The corresponding column 1, 3, and 5 from the original matrix A form the column space of ref(A).

2. Relevant equations

3. The attempt at a solution

(a) and (b) are straight forward and hence, both are true. I think (c) is false. Not sure about (d) though.

For (c), I have a specific counter example. I have column space of ref(A) is something like {[1 0 0 0], [0 1 0 0], [0 0 1 0]}, whereas the column space of the original matrix A is {[1 3 2 -1], [-2 2 3 2], [3 1 2 4]}. Notice that the 4th entry for the space spanned by ref(A) will always be 0, but it's possible to have a non-zero value for the space spanned by the column space, if the answers are taken from the original matrix A.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Column Space of Matrix A and ref(A)

**Physics Forums | Science Articles, Homework Help, Discussion**