Okay, whatisthe "Invertible Matrix Theorem"?

This is confusing, you said above that vThis is what I have so far:

Let A be invertible. We want to show {v_{1}, v_{2}, ... v_{n}} is linearly independent. {v_{1}, v_{2}, ... v_{n}} is the standard basis for R^{n}._{1}, v_{2}, ...., v_{n}were the columns of A. Now you are saying they are the standard basis for R^{n}.

Which do you want?

Then you say "Let c be in the reals" but talk about cLet c be in the reals. Then set c_{1}v_{1}+ c_{2}v_{2}+ ... + c_{n}v_{n}= the zero vector. Then

[c_{1}] = the zero vector = [0]

[c_{2}] [0]

[c_{n}] [0]

Thus, {v_{1}, v_{2}, ... v_{n}} is linearly independent.

I'm not sure if this is right or how to complete the second half of the proof. Any help would be appreciated!_{1}, c_{2}, ..., c_{n}. Did you mean "c_{i}" rather than just i?

And what do you mean by "[c_{1}] = the zero vector = [0]"? What does the "[ ]" indicate?