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8. Find the eigenvalues of -7 6 0 0 -12 12 11 For each eigenvalue find a basis for the corresponding eigenspace. 9. For each of the following functions, determine whether they give a real inner product. Give reasons for your answers. (a) h-,-i on R3 given by hx, yi = xiyz + x3y2 + Xzy2. (b) h-,-i on M(2,2) given by hA, Bi = tr(BA). (c) h-,-i on P2 given by hp, qi = p(0)q(0) + 2p(1)q(1) + 3p(2)q(2). 10. Use the Gram-Schmidt method to form an orthonormal basis for M(2,2) with inner product hA, Bi = tr(BTA) from the set of basis elements