Need some help with understanding this question:
If we have a matrix A and y where y=[-5
A=[1 0 1 0 3
0 1 0 0 2]
0 0 0 1]
Q. Is y in the range of A?

Question

Need some help with understanding this question:
If we have a matrix A                and y where y=[-5
A=[1 0 1 0                                                             3
      0 1 0 0                                                             2]
      0 0 0 1]                                                  
Q. Is y in the range of A?

anonymous · Answer

Well the matrix spans R3, so all vectors in R3 are in the range of A

anonymous · Answer

And it spans R3 because you have (at least) three linearly independent columns

anonymous · Answer

So if the matrix A only had 2 L ID columns then this same (y) would not be in the range of A?

anonymous · Answer

It might be, you'd have to try to write y as a linear combination of the vectors of A. All I'm saying here is you can give me any 3 dimensional vector and I can say for sure that it's in the range.

anonymous · Answer

For example if A= 
[1,0,3]
[0,1,0]
[0,0,0]

and y=
(2
 3
 0)

Then y is in the range of A because it's equal to 2*a1+3*a2+0*a3. If you can write the vector as a linear combination of the columns, it's in the range.

anonymous · Answer

Thank you for your help!! I think I am finally understanding this!