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...
Homework Statement
If V is the orthogonal complement of W in Rn, is there such a matrix with row space V and nullspace W? Starting with a basis for V, construct such a matrix.
The Attempt at a Solution
I've been trying to use the fact that V is the left nullspace of the column space of W...
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]...
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...