Linear algebra - transformations

[Niles]

[SOLVED] Linear algebra - transformations

Homework Statement

Please take a look at:

http://www.math.luc.edu/~jdg/w3teaching/math_212/sp02/PDF/test2practice.pdf

Please take a look at #7, question c. To determine if the vector w is in the image (range) of T, I find the matrix B that represents the linear transformation T and find the solution to the system:

Bx = w,

because w has to be in the span of B (which I found to be the image of T). If it is consistent, w is in the range of T?

Thanks in advance,

sincerely Niles.

 

[HallsofIvy]

It's not clear to me what the "span" of a matrix would be! I think you mean the span of the vectors making the columns of the matrix T. Yes, that span, the "column space" of T is the image of the T and "image" is the "range" here. The crucial point is exactly how you show that w is in the image of T.

 

[Niles]

I have the vectors that span the column space. I put these vectors together in a matrix I call B, and I write a new matrix <B|w>, and solve this. If consistent, w is in the column space.

Correct?