In each case, show that T is symmetric and find an orthonormal basis of eigenvectors of T.
(a) T:(R3→R3; T(a, b, c) = (2a + 2r, 3b, 2a + 5c)-, use the dot product
(b) T: R3 →R3; T(a, b, c) = (7a - b, -a + 7,b,2c); use the dot product
(c) T: P2 → P2 T(a + bx + cx2) = 3b + (3a + 4c)x'+4bx2 inner product (a + bx + cx2), =aa' + bb' + cc
(d) T: P2 → P2;
T(a + bx + ex') = (c - a) + 3bx + (a- c)x; inner product as in part (c)