Question: In each case, show that T is symmetric by calculating MB(T) for some orthonormal basis B. (a) T:R3 R3; T(a, b, c) = (a-2b, -2a

In each case, show that T is symmetric by calculating MB(T) for some orthonormal basis B.
(a) T:R3 †’ R3;
T(a, b, c) = (a-2b, -2a + 2b + 2c, 2b-c); dot product
(b) T:M22 †’ M22;

(c) T: P2 †’ P2; T(a + bx + cx2)
= (b + c) + (a + c)x + (a + b)x2; inner product
(a + bx + cx2, a + b'x + cx2) = aa'+ bb'+cc

inner product

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