Two brothers went shopping at a back-to-school sale were all shirts were the same price, and all the shorts too. The younger brother spent $145 on 3 new shirts and 10 pairs of shorts. The older brother purchased 4 new shirts and 10 pairs of shorts and paid a total of $150. How much did each item cost?

To diagonalize an nxn matrix a means to find an invertible matrix p and a diagonal matrix d such that a pdp d p ap or [1 3 dh epap 3 let a=-3 -5 -3 3 3 1 step 1: find the eigenvalues of matrix a "2's" step 2: find the corresponding eigenvectors of a step 3: createp from eigenvectors in step 2 step 4 create d with matching eigenvalues.