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Prove that the given set B is a basis for the given vector space V. And then, determine if the given vector is in V. If so, find the coordinate vector of ✔ with respect to B. a) B = 0 2 { (²9) · (₂2)⋅ ( ) ( ) }· 2 1 1 V = M₂2x2 (R), v = 5 (₁2) 1 -1 2 b) 8 = {(1, 2) - ( 7² )} V - Spa(8), (1²3) B= = v = 0 -1 1 1 0 2 (c) B = {1, 1+ 2X, 1+ 2X +3X², 1+ 2X + 3X² + 4X³}, V = R³(X), v = 8X³

Prove that the given set B is a basis for the given vector space V. And then, determine if the given vector is in V. If so, find the coordinate vector of ✔ with respect to B. a) B = 0 2 { (²9) · (₂2)⋅ ( ) ( ) }· 2 1 1 V = M₂2x2 (R), v = 5 (₁2) 1 -1 2 b) 8 = {(1, 2) - ( 7² )} V - Spa(8), (1²3) B= = v = 0 -1 1 1 0 2 (c) B = {1, 1+ 2X, 1+ 2X +3X², 1+ 2X + 3X² + 4X³}, V = R³(X), v = 8X³

Advanced Engineering Mathematics
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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solve parts a, b, and c
2. Prove that the given set B is a basis for the given vector space V. And then, determine if the given vector v is in V. If so, find the coordinate vector of v with respect to B. (a) B = { ( ) ( ))⋅ ( ² ) · ( ) } " (b) B = V = M2x2 (R), V = 1 -1 { ( 1 ) · G 9) ·( 1 )} -1 (c) B = {1, 1+ 2X, 1 + 2X +3X², 1+ 2X +3X² + 4X³}, V = R3(X), v = 8X³ 5 (₁22) -2 V = Span(B), v = (1 2 3)
Transcribed Image Text:2. Prove that the given set B is a basis for the given vector space V. And then, determine if the given vector v is in V. If so, find the coordinate vector of v with respect to B. (a) B = { ( ) ( ))⋅ ( ² ) · ( ) } " (b) B = V = M2x2 (R), V = 1 -1 { ( 1 ) · G 9) ·( 1 )} -1 (c) B = {1, 1+ 2X, 1 + 2X +3X², 1+ 2X +3X² + 4X³}, V = R3(X), v = 8X³ 5 (₁22) -2 V = Span(B), v = (1 2 3)
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