2. Given the quadratic form Let 12 X = A = 12 -6 and Q(x) = x' Ax = 3r; + 240102 -617. I2 Do the following steps: a. Compute the eigenvalues for the matrix A. b. Compute basis vectors for each eigenspace. c. Show that the eigenspaces are orthogonal. d. Normalize the eigenvectors and write down a matrix S such that S-1 = ST. e. Calculate B = S"AS, which will be diagonal with the eigenvalues on the diagonal (if your previous steps are correct). f. Define u = S'x, and compute Q(u) = uBu. g. Classify the quadratic form @ as to whether it is positive definite, negative definite, or indefinite