Let T : P2(R) P2(R) be the linear transformation satisfying: T (x2 1) = x2 + x 3, T (2x)
Chapter 6, Problem 33(choose chapter or problem)
Let T : P2(R) P2(R) be the linear transformation satisfying: T (x2 1) = x2 + x 3, T (2x) = 4x, T (3x + 2) = 2(x + 3). Find T (1), T (x), T (x2), and hence show that T (ax2 + bx + c) = ax2 (a 2b + 2c)x + 3c, where a, b, and c are arbitrary real numbers.
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