Let V₁, V₂ be vectors in R³ given by ---- V1 a) Find a vector w R³ with the following properties: • w / 0 • For any linear transformation T: R³ R³ which satisfies T(v₁) = T (V₂) we must have T(w) = 0. Enter the vector w in the form [C₁, C₂, C3]: d₁ b) Find a vector z = d₂ with the following properties: d3 Enter the vector z in the form [d₁, d₂, d3]: V2 • d₁ = 0 • For any linear transformation T: R³ R³ which satisfies T (V₁) = T(v₂) we must have T(z) = T(v₁) = T (v₂). Hint. Use part a).

Let V₁, V₂ be vectors in R³ given by ---- V1 a) Find a vector w R³ with the following properties: • w / 0 • For any linear transformation T: R³ R³ which satisfies T(v₁) = T (V₂) we must have T(w) = 0. Enter the vector w in the form [C₁, C₂, C3]: d₁ b) Find a vector z = d₂ with the following properties: d3 Enter the vector z in the form [d₁, d₂, d3]: V2 • d₁ = 0 • For any linear transformation T: R³ R³ which satisfies T (V₁) = T(v₂) we must have T(z) = T(v₁) = T (v₂). Hint. Use part a).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 16RQ

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