Recent content by junsugal

Homework Statement This problem will guide you through the steps to obtain a numerical approximation of the eigenvalues, and eigenvectors of A using an example. We will define two sequences of vectors{vk} and {uk} (a) Choose any vector u \in R2 as u0 (b) Once uk has been determined, the...

hmm, what do you mean by start with x4? For part(a) I said that yes the function is isomorphic because P4 and R5 both have dimension of 5. And according to one of the properties of isomorphic, the dimensions of 2 vector spaces should be the same. Thanks for the tips! :)

Hi :) It is Col(A). I thought it means that Nul(A) is a subspace of Col(A)? well, I'm still confused though. I tried to solve this problem asuming that A is zero matrix. Because I couldn't think of any nxn matrix that will get zero after multiply by itself.

Homework Statement Consider the linear function F : P4 -> R5 that sends the basis {1,x,x2,x3,x4} of P4 to the basis {e1,e1,e3,e4,e5} in R5, in that order , that is F(xn)= e(n+1)). (a) Is this function an isomorphism? (b) Consider the linear function D : P4-> P4...

Homework Statement Prove that if A is a nxn matrix such that A^2=0, then Col(A) is a proper subset of Nul(A) Homework Equations The Attempt at a Solution None, i have no idea how to start. Please guide me or explain what does the question means and how to approach.

Homework Statement Consider the matrix A = 1 1 2 1 1 2 3 4 2 4 7 2t-6 2 2 6-t t Find the values of t for which the matrix A is invertible Homework Equations...