Recent content by Haystack

I really appreciate all the help with this one y'all. Thanks.

Yes it is a basis. But I'm not sure I follow. In that case wouldn't [L] just be the columns of L(v1), L(v2), ... L(vn)?? I think my problem is that I keep thinking of this as matrix multiplication when it's not

Hey thanks for the replies. Somehow I found L. Although I'm not 100% clear on how I did it... I started with a matrix of the original vectors that L was acting on, times some 4x4 matrix, and set it equal to a matrix with the solutions of L(v1), L(v2), etc... but transposed. |1 1 1 1||a b c d|...

Any ideas to get me started at least?

Homework Statement Let L be a linear operator such that: L[1, 1, 1, 1] = [2, 1, 0, 0] L[1, 1, 1, 0] = [0, 2, 1, 0] L[1, 1, 0, 1] = [1, 2, 0, 0] L[1, 0, 1, 1] = [2, 1, 0, 1] a) Find [L] b) Compute L[1, 2, 3, 4] Homework Equations The Attempt at a Solution I used another...

Thanks for the replies. Although, I'm not sure I understand your basis HallfofIvy. I can't seem to find how it's related to the one I ended up with. I understand how you got there with the substitution, but is it just another basis for S?

Homework Statement Let S = [x y z w] \in R^4 , 2x-y+2z+w=0 and 3x-z-w=0 Find a basis for S. Homework Equations The Attempt at a Solution I started by putting the system into reduced row form: [2 -1 2 1] [3 0 -1 -1] [2 -1 2 1] [0 3 -8 -5] [6 0 -2 -2]...