Problem 4. Consider the vectors in R4 1 4 01 = U2 = 8 U3 = 9. 10 3c where c E R is a scalar. (a) Find all the values of c e R such that the vectors 1, 72, 03 are linearly dependent. For each value of c obtained in (a), find a linear combination of the vectors 1, 02, 03 that equals 0 with not (b) all zero coefficients (the coefficients must be actual numbers, not variables).

Problem 4. Consider the vectors in R4 1 4 01 = U2 = 8 U3 = 9. 10 3c where c E R is a scalar. (a) Find all the values of c e R such that the vectors 1, 72, 03 are linearly dependent. For each value of c obtained in (a), find a linear combination of the vectors 1, 02, 03 that equals 0 with not (b) all zero coefficients (the coefficients must be actual numbers, not variables).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 33EQ

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