Amanda, Bruno and Carla collected bottle caps for charity. Amanda collected (4f - 3) bottle caps. Bruno collects twice as many bottle caps as Amanda. Carla collects 3(5 + 2f) bottles. How many bottles did they collect altogether in terms of f .

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.