Q1. Let M be the following matrix:
(a) Find the inverse of M.
To find the inverse of M, we need to find det(A).
det(A) = ad - bc
where
det(A) = ad - bc = (2*1) - (-3)(-2) = (2)-(6) = -4
Then, rearrange M
Multiply by 1/det(A)
This gives M^-1 of:
(b) Using your answer to (a) or otherwise, find the solution to the following system of equations:
2 ways of solving this question.
1) Using M^-1
2) Using Row Reduction / Subtraction
(c) Find the eigenvalues of M and their corresponding eigenvectors.
(d) Write down matrices D and P such that D is a diagonal matrix and M = PDP^-1
Important:
For the eigenvalue in first column D should match the eigenvector in the first column of P
i.e. If lambda1 is in the first column of D, the eigenvector of the corresponding lambda should come in the first column of P.