Question

Determine if w is in Col A. is w in Nul A?

Answer 1

A=
10 -8 -2 -2
0 2 2 -2
1 -1 6 0
1 1 0 -2

w=
2
2
0
2

Answer 2

the easiest one to check is if its in the null space. Calculate:\[Aw\]if it comes out to zero, then w is in the Null Space.

Answer 3

thanks! how do I determine if its in Col A?

Answer 4

You need to create the augmented matrix:\[[A\mid w]\] and row reduce it to see if you get a solution to the equation:\[Ax=w\]If there exists and x that satisfies this matrix equation, then w is in the Column Space of A.

Answer 5

my final matrix is
1 0 0 -1 1
0 1 0 -1 1
0 0 1 0 0
00000

that means that w is in col A right?

Answer 6

yes thats correct. in fact, that lets us know that w is actually one of the first column plus 1 of the second column.