2. Define two ordered bases B = and E = on R³. (i) Find the vector vị of R³ whose component vector with respect to B is [V1]B = 2 and write its component vector [V1]E with respect to E. (ii) Find the 3 × 3 change-of-basis matrix PE-B. Check your answer by computing [vi]E = PE-B[Vi]B, and comparing to what you found in part (i). (iii) Invert PE-B to find PBE. Then use PBte to find the component vector [v2]B of V2 relative to B.

2. Define two ordered bases B = and E = on R³. (i) Find the vector vị of R³ whose component vector with respect to B is [V1]B = 2 and write its component vector [V1]E with respect to E. (ii) Find the 3 × 3 change-of-basis matrix PE-B. Check your answer by computing [vi]E = PE-B[Vi]B, and comparing to what you found in part (i). (iii) Invert PE-B to find PBE. Then use PBte to find the component vector [v2]B of V2 relative to B.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.3: Change Of Basis

Problem 2EQ

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