# Diagonizable Matrix, Inverse and Nullspace

1) If a Matrix A is diagonizable, must it have an inverse ? if so, is it diagonizable? Can {see attachment} be diagonized, does it have an inverse as well as {see attachment}

2) A is mxn

For m<n, is there a vector b such that Ax = b does not have any solution? Any trivial solution for Ax = 0?

b) Can say the same for m>n ? Any possible dimension for nullspace of A?

https://brainmass.com/math/linear-algebra/diagonalizable-matrix-inverse-nullspace-30836

#### Solution Summary

Diagonizable Matrices, Inverses and Nullspaces are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.

$2.19