Problem 2 Consider the following matrix B: 1 -2 0 17 3 -2 1 -5 20 -2 0 1 B = -2 3 a. Find R(B). b. Find N(B). c. Using R(B) and N(B) find an example f for which Bw = f has no solution.

Consider the following equation where A is n x m matrix: AX = Y If n 2m, what can be said about the number of possible solutions to AX = Y

PLEASE Provide an easy to follow, step-by-step, detailed, and concise solution for the following problem..

I need help with part b.

Please don't provide handwritten solution ....

Problem 4. 1 -3 a) Is the matrix A = 2 0 diagonalizable? 1 -3 b) For which k is the matrix A = k 12 1 -3 diagonalizable? 2 1 -3 c) Find a 3 x 3 matrix A, which is not the identity or the zero matrix, such that A4 = A³.