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?

Question

phi · Answer

use elimination to find the pivot columns.

anonymous · Answer

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...

anonymous · Answer

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

anonymous · Answer

R1-R3

anonymous · Answer

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

anonymous · Answer

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...

phi · Answer

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

phi · Answer

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

anonymous · Answer

thanks

phi · Answer

btw, dumb book!

anonymous · Answer

agree!