Let S denote the standard basis of R² and let B = {b1, b2} be some other basis of R². Suppose that 1 [V3 -1 PB,S 2 1 (i) Express x = (1,1) as a linear combination of the vectors in B. x = (V3 - 1) b1 + (V3+1) b2 x = v3 /2 b1 + V3/2 b2 x = v3 - 1/2 b1 + v3+1/2 b2 x = (V3 - 1) /2 b1 + (V3+1)/2 b2

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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Let S denote the standard basis of R² and let B =
{b1, b2} be some other basis of R².
Suppose that
1 [V3 -1
PB,S
2
1
(i) Express x =
(1, 1) as a linear combination of the vectors in B.
x = (V3 - 1) b1 + (v3+1) b2
X = v3 /2 b1 + v3/2 b2
x = v3 - 1/2 b1 + v3+1/2 b2
x = (V3 - 1) /2 b1 + (V3+1)/2 b2
Transcribed Image Text:07 Let S denote the standard basis of R² and let B = {b1, b2} be some other basis of R². Suppose that 1 [V3 -1 PB,S 2 1 (i) Express x = (1, 1) as a linear combination of the vectors in B. x = (V3 - 1) b1 + (v3+1) b2 X = v3 /2 b1 + v3/2 b2 x = v3 - 1/2 b1 + v3+1/2 b2 x = (V3 - 1) /2 b1 + (V3+1)/2 b2
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