2. Let S P₂(R) P2(R) be given by S(f)(x) = xf'(x), and let T P2(R) R² be given by T(g) = (g(1), g(2)). (a) Given an explicit formula for (TS)(ax² + bx + c). (b) Let B = {1, x, x²} and B' = {(1, 0), (0, 1)} be the standard bases for P2(R) and R2 respectively. Calculate directly each of the matrices and then verify the formula [TE, [S] [TS] B' [TS] B = [T]B[S] B by calculating the matrix multiplication.

University Physics Volume 3
17th Edition
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:William Moebs, Jeff Sanny
Chapter7: Quantum Mechanics
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Problem 7.1CYU: Check Your Understanding If a=3+4i , what is the product a* a?
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2. Let S P₂(R) P2(R) be given by
S(f)(x) = xf'(x),
and let T P2(R) R² be given by
T(g) = (g(1), g(2)).
(a) Given an explicit formula for (TS)(ax² + bx + c).
(b) Let B = {1, x, x²} and B' = {(1, 0), (0, 1)} be the standard bases for P2(R) and
R2 respectively. Calculate directly each of the matrices
and then verify the formula
[TE, [S] [TS] B'
[TS] B = [T]B[S] B
by calculating the matrix multiplication.
Transcribed Image Text:2. Let S P₂(R) P2(R) be given by S(f)(x) = xf'(x), and let T P2(R) R² be given by T(g) = (g(1), g(2)). (a) Given an explicit formula for (TS)(ax² + bx + c). (b) Let B = {1, x, x²} and B' = {(1, 0), (0, 1)} be the standard bases for P2(R) and R2 respectively. Calculate directly each of the matrices and then verify the formula [TE, [S] [TS] B' [TS] B = [T]B[S] B by calculating the matrix multiplication.
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