6. Let V = span{1+ x², x}. Two ordered bases for V are Si = {1+x², x} and S2 = {1+x + x?, 2 + x + 2x²}. The function f(x) = 5+ 3x + 5x² has component vector with respect to the basis S1. Find the 2 x 2 change-of-basis matrix Ps,-s, . What is the component vector of f(x) with respect to S2?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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6. Let V = span{1+ x², x}. Two ordered bases for V are
Si = {1+x², x}
and
S2 = {1+x + x?, 2 + x + 2x²}.
The function f(x)
= 5+ 3x + 5x² has component vector
with respect to the basis S1. Find the 2 x 2 change-of-basis matrix Ps,-S,. What is the
component vector of f(x) with respect to S2?
Transcribed Image Text:6. Let V = span{1+ x², x}. Two ordered bases for V are Si = {1+x², x} and S2 = {1+x + x?, 2 + x + 2x²}. The function f(x) = 5+ 3x + 5x² has component vector with respect to the basis S1. Find the 2 x 2 change-of-basis matrix Ps,-S,. What is the component vector of f(x) with respect to S2?
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