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A. Given vectors a1 = , a2 = , аз -3 determine the components of the vector 4 2а1 + За2 — 5аз. B. Let ui = and u2 = -1 3 a. Calculate the linear combination of u1 and uz with corresponding weights (scalar multiples) 1 and 2. The resulting vector is a vector which can be written as a linear combination of uj and u2. b. Can vị = be written as a linear combination of uj and u2? If so, which linear combination? If not, explain why not.

A. Given vectors a1 = , a2 = , аз -3 determine the components of the vector 4 2а1 + За2 — 5аз. B. Let ui = and u2 = -1 3 a. Calculate the linear combination of u1 and uz with corresponding weights (scalar multiples) 1 and 2. The resulting vector is a vector which can be written as a linear combination of uj and u2. b. Can vị = be written as a linear combination of uj and u2? If so, which linear combination? If not, explain why not.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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3 2 1 A. Given vectors a1 = -1 , a2 = determine the components of the vector az = -3 4 2а1 + За2 — 5аҙ. 2 B. Let ui = 1 and u2 = 1 a. Calculate the linear combination of u1 and u2 with corresponding weights (scalar multiples) 1 and 2. The resulting vector is a vector which can be written as a linear combination of uj and u2. b. Can vị = be written as a linear combination of uj and u2? If so, which linear 4 combination? If not, explain why not.
Transcribed Image Text:3 2 1 A. Given vectors a1 = -1 , a2 = determine the components of the vector az = -3 4 2а1 + За2 — 5аҙ. 2 B. Let ui = 1 and u2 = 1 a. Calculate the linear combination of u1 and u2 with corresponding weights (scalar multiples) 1 and 2. The resulting vector is a vector which can be written as a linear combination of uj and u2. b. Can vị = be written as a linear combination of uj and u2? If so, which linear 4 combination? If not, explain why not.
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