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Changing basis in order to diagonalize a matrix

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Suppose that the matrix A is a linear operator on R(2) represented in the standard basis {i,j}, by the matrix
mat(A)= [-1 3;2 4].

Find a new basis in which A is diagonalized.

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Solution Summary

A step-by-step solution is provided which illustrates how to change basis while diagonalizing a matrix. A 2x2 matrix is used as an example

Solution Preview

See attachment for a step-by-step solution using a 2x2 matrix as an example used to illustrate the process.

Diagonalize A
So, the first step in solving this problem is to solve the mini- problem of det(A-lamda*I)=0
This will yield the eigenvalues of A.
Next, we need to find the eigenvectors ...

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