G f(1,1) f(-1,1)Given contour map of z = f(x, y), sketch the gradient vectors (with approximate length and direction): ∇f(1, 1), ∇f(1, −1), ∇f(−1, 1), and ∇f(−1, −1). Describe, how you choose the direction and the length of the gradient vector in each case.

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.