If w₁, w2, w3 are independent vectors, show that the sums v₁ = w2 + w3 andv2 = wi+w3 and v3 = w₁+w2 are independent. (Write c₁v₁+c2v2+c3v3 = 0in terms of the w's. Find and solve equations for the c's, to show they are zero.)

We say the vectors u,v and w are independent if then a=b=c=0.here a,b and c are constants.

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.)

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.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 18EQ

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Question

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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