Data Science

Matrix Calculations, Eigen Vector

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



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




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.