If w₁, w2, w3 are independent vectors, show that the sums v₁ w₂+w3 and v2 wi+w3 and v3 w₁+w2 are independent. (Write c₁v₁+22+C3V3=0 in terms of the w's. Find and solve equations for the c's, to show they are zero.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 12E
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If w₁, w2, w3 are independent vectors, show that the sums v₁ = w2 + w3 and
v2 = wi+w3 and v3 = w₁+w2 are independent. (Write c₁v₁+c2v2+c3v3 = 0
in terms of the w's. Find and solve equations for the c's, to show they are zero.)
Transcribed Image Text:If w₁, w2, w3 are independent vectors, show that the sums v₁ = w2 + w3 and v2 = wi+w3 and v3 = w₁+w2 are independent. (Write c₁v₁+c2v2+c3v3 = 0 in terms of the w's. Find and solve equations for the c's, to show they are zero.)
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