- #1
blue4123
- 3
- 0
Homework Statement
For which ##2x2## matrices ##A## does there exist an invertible matrix
##S## such that ##AS=SD##, where
##D=
\begin{bmatrix}
2 & 0\\
0 & 3
\end{bmatrix}
##?
Give your answers in terms of the eigenvalues of ##A##.
Homework Equations
##A\lambda=\lambda\vec{v}##
The Attempt at a Solution
S is a ##2x2## matrix. If x and y are the 1st and second columns of A, then we can write the following:
Ax=2x
Ay=3y
So we can see from these two equations that 2 and 3 must be the corresponding eigenvalues of A and their respective eigenvectors must be linearly independent.I was hoping someone could critique my solution attempt as I am not too confident that I fully answered the question or if there's a better way to express my answer