3. Let V = R3 and let B = (b1, b2, b3), where b₁ = 1 b₂ = 0 b3 = (a) Prove B is a basis of V over R. (b) For u = 2 find the column vector [u]B. 3 ዐ1 (c) For v = 02 find a formula for the column vector [v]B in terms of a1, a2, a3. 13

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 36E
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3. Let V = R3 and let B = (b1, b2, b3), where
b₁ =
1
b₂ =
0
b3 =
(a) Prove B is a basis of V over R.
(b) For u =
2
find the column vector [u]B.
3
ዐ1
(c) For v =
02
find a formula for the column vector [v]B in terms of a1, a2, a3.
13
Transcribed Image Text:3. Let V = R3 and let B = (b1, b2, b3), where b₁ = 1 b₂ = 0 b3 = (a) Prove B is a basis of V over R. (b) For u = 2 find the column vector [u]B. 3 ዐ1 (c) For v = 02 find a formula for the column vector [v]B in terms of a1, a2, a3. 13
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