Question

Can someone please help? What is a basis for the column space of matrix A = [ 1,2,0,1; 0,1,1,0; 1,2,0,1]? Why?

Answer 1

use elimination to find the pivot columns.

Answer 2

I did and got that x1 and x3 are pivot columns, but according to the solution they are x1 and x3, and don't know why...

Answer 3

\[\left[\begin{matrix}1 & 2 & 0 & 1 \\ 0 & 1 & 1 & 0\\ 1&2&0&1\end{matrix}\right]\]

Answer 4

R1-R3

Answer 5

\[\left[\begin{matrix}1 & 2 & 0 & 1 \\ 0 & 1 & 1 & 0\\ 0&0&0&0\end{matrix}\right]\]

Answer 6

that's right... that's what I have... so I said the first two columns were the basis, but supposedly it is the first and third...

Answer 7

You are not wrong. However, you could use any 2 independent columns.

Answer 8

clear col 4 equals col 1, so you can not use col1 and col4

Answer 9

thanks

Answer 10

btw, dumb book!

Answer 11

agree!