Question

Linear algebra e^A matrix summation

Answer 1

i will now post the problem

Answer 2

image is attached

Answer 3

What's your question?

Answer 4

oh i need to know how to find matrix Q

Answer 5

matrix Q is special because if you do Q^-1AQ then the result must be a diagonal matrix.

Answer 6

Yeah, Q is a matrix of eigenvectors of the matrix A. The diagonal matrix is the eigenvalues of A. Have you ever diagonalized a matrix before?

Answer 7

For example, take the first column of Q and multiply it by A we get: \[\left[\begin{matrix}1 & 4 \\ 2 & 3\end{matrix}\right] \left[\begin{matrix}1 \\ 1\end{matrix}\right] = 5\left[\begin{matrix}1 \\ 1\end{matrix}\right]\] So that proves that the vector (1,1) is an eigenvector of the matrix A with eigenvalue 5 in case you were wondering.