CUNY605-Assignment 3 Solved

1. Problem set 1

(1)   What is the rank of the matrix A?

                                                                            1      2      3        4 

A = −01 01 −12  31                (1) 5      4 −2 −3

(2)   Given an mxn matrix where mn, what can be the maximum rank? The minimum rank, assuming that the matrix is non-zero?

(3)   What is the rank of matrix B?

                                                                                                                                            (2)

2. Problem set 2

Compute the eigenvalues and eigenvectors of the matrix A. You’ll need to show your work. You’ll need to write out the characteristic polynomial and show your solution.