3. Given the two ordered bases U, V below for R³ (also the standard basis E = [e1, €2, €3]) (): 1 (3) U: U2 · U3 1 4 1 V = 1 , V3 = 1 Vi = , V2 = -2 (a) For x = 3 u1+2 u2 – 4 u3, find the coordinate vector [x]u of x with respect to the U basis. (b) For the same x above, find the coordinate vector [x]y of x with respect to the V basis.

3. Given the two ordered bases U, V below for R³ (also the standard basis E = [e1, €2, €3]) (): 1 (3) U: U2 · U3 1 4 1 V = 1 , V3 = 1 Vi = , V2 = -2 (a) For x = 3 u1+2 u2 – 4 u3, find the coordinate vector [x]u of x with respect to the U basis. (b) For the same x above, find the coordinate vector [x]y of x with respect to the V basis.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 32EQ

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