Let S = {a+bx+cx²: = {V1, V2, V3} and T a, b, c = R}, where v₁ = 1 + x + 3x², v₂ = −2 − 2x – 7x², v3 = 1 + 2x + 6x² and {w₁, W2, W3} be two bases in the vector space P₂ w₁ = 1 + x − x², W₂ = 1 + 2x², w3 = 3− x+5x2. = Find the transition matrix from T to S. Let v = = 2v₁ - 3v2 + V3, find the coefficients (C₁, C2, C3) so that v = C₁W₁ + C2W2 + C3W3. Hint: For the second part, you need also to find the transition matrix from S to T.
Let S = {a+bx+cx²: = {V1, V2, V3} and T a, b, c = R}, where v₁ = 1 + x + 3x², v₂ = −2 − 2x – 7x², v3 = 1 + 2x + 6x² and {w₁, W2, W3} be two bases in the vector space P₂ w₁ = 1 + x − x², W₂ = 1 + 2x², w3 = 3− x+5x2. = Find the transition matrix from T to S. Let v = = 2v₁ - 3v2 + V3, find the coefficients (C₁, C2, C3) so that v = C₁W₁ + C2W2 + C3W3. Hint: For the second part, you need also to find the transition matrix from S to T.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let S =
=
{V₁, V2, V3} and T {W₁, W2, W3} be two bases in the vector space P₂
{a+bx+cx² : a, b, c = R}, where
V₁ = 1+x+3x², v₂ = -2 2x − 7x², V3 = 1 + 2x + 6x²
and
W₁ = 1 + x - x², W₂ = 1 + 2x², W3 = 3−x+5x².
W1
Find the transition matrix from T to S. Let v = 201
(C₁, C2, C3) so that v = : C₁W₁ + C₂W2 + C3W3.
Hint: For the second part, you need also to find the transition matrix from S to T.
=
· 3v2 + v3, find the coefficients
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