Recent content by starcoast

Homework Statement Suppose A = SΛS^{-1}. What is the eigenvalue matrix for A + 2I? What is the eigenvector matrix? Check that A + 2I = ()()()^{-1}. The Attempt at a Solution I think I'm pretty close I'm just not sure what to do next: A + 2I = SΛS^{-1} + 2I = SΛS^{-1} + 2SS^{-1} ? now...

First of all, let me apologize if this question is in the wrong place. It's fundamentally a statistics question but it relates to computer science. I'm also not sure if this falls under the "homework" category, since it's for a class, but I need assistance on a general idea, not a problem set...

nevermind, I figured it out

Homework Statement Find a basis for the orthogonal complement of the row space of A: A = [1 0 2 1 1 4] Split x = (3,3,3) into a row space component xr and a nullspace component xn. The Attempt at a Solution For the first part of the problem I took A to RREF R = [1 0 2 0 1 2]...

Thank you! I should have guessed that.

Homework Statement Prove that T^{2} is a linear transformation if T is linear (from R^{3} to R^{3}. So I understand when a transformation is considered linear, but I don't understand what squaring a transformation does. I don't think it means squaring the result of the transformation but...

Okay, I used that bijection instead of induction, but something about it doesn't feel like I proved it for all n. How does this look? We divide the subsets of a given n-element set T into two sets: the set of subsets that contain the nth element in the set, S, and the set of subsets that do...

Homework Statement How is the number of subsets of an n-element set related to the number of subsets of an (n-1) element set? Prove that you are correct. Homework Equations The Attempt at a Solution So, clearly the the number of subsets in an n element set is 2^{n}. So the number...