Can someone help me check if this matrix is diagonalisable?
#[(4,5), (2,3)]#
1 Answer
See below
Explanation:
From the characteristic equation:
Solve the quadratic for eigenvalues:
#lambda_(1,2) = (7 pm i sqrt(39))/2#
These will deliver 2 distinct eigenvectors so you can diagonalise .
For eigenvectors

#implies 4 x  5 y = (7 + i sqrt(39))/2 x# 
#5y = (8  7  i sqrt(39))/2 x#
A first eigenvector is:
For the second:
#4 x  5 y = (7  i sqrt(39))/2 x#
A second eigenvector is: