So I have a test on Monday and my professor posted a couple of non-graded review questions that she said we should look over. Anyhow, I have a couple of questions that I'd like answered if that's okay. I'm not looking for complex proofs or anything, just a simple explanation. :)
*If A is invertible, is A-Transpose also invertible? If so, what is (A^T)^-1?
My guess is that A-Transpose would also be invertible because of the determinant. Though I don't think my teacher will like this answer because we haven't covered determinants.
*Why are elementary matrices important for the Inverse Algorithm?
I'm assuming that the answer here is simple, in that elementary row operations are used for row-reduction so that's why they are important.
*Is it possible that all solutions of a homogeneous system of ten linear equations in twelve variables are multiples of one fixed nonzero explanation?
I'm assuming this is possible, but I'm not sure why....
*Suppose that A is a 5x11 matrix. What is the smallest dimension for Nul(A)?