Recent content by TorcidaS

Homework Statement Let P1 and P2 be the projections defined on R^3 by: P1(x1, x2, x3) = (1/2(x1+x3), x2, 1/2(x1+x3)) P2(x1, x2, x3) = (1/2(x1-x3), 0, 1/2(-x1+x3)) a) Let T = 5P1 - 2P2 and determine if T is diagonalizable. b) State the eigenvalues and associated eigenvectors of T...

Homework Statement Find the matrix of f relative to Alpha' and Beta'. Alpha' = [(1,0,0), (1,1,0), (2,-1,1)] Beta' = [(-13,9), (10,-7)] The question originally reads that f is a bilinear form. I've found a (correct according to answer key) matrix A that is 3 -4 4 -5 -1 2...

Hi, thank you very much for your answer.

Homework Statement Let T be the linear transformation of R5 into R3 that has the matrix A = 1 3 2 0 -1 2 6 4 6 4 1 3 2 2 1 relative to the bases [(1,1,1,1,1), (1,1,1,1,0), (1,1,0,0,0), (1,0,0,0,0), (0,0,0,0,1)] of R5 and [(1,1,1), (0,1,0), (1,0,0)] of R3. Find a basis for the range...

Hi, could you just help me with the part where they write it wrt to the basis? It sort of confuses me. I understand we get (-5/4 1), and once clearing the fraction we get (-5, 4). But how does this jump to (-5, -6)?