(2) [7 points] Given that the eigenvalues for matrix A shown below are 2₁=1, 22-2, and 23-3, find all corresponding eigenvectors. Next, diagonalize A by finding matrices S and A such that A = SAS-¹, where A is a diagonal matrix. Do all work by hand, except basic row reductions and computation of a matrix inverse.
4 -3
3 1
0 2
-2