Consider the two Dases S 3 {(1,0, 0), (0, 1,0), (0,0, 1)} and в — {(1,0, 1), (0, -1,2), (2, 3, —5)} for R' (Hint: Throughout this problem, refer to section 5 in the notes on Canvas, or the relevant sections in your textbook). (a) Find the transition matrix P 1 from the standard basis S to the nonstandard basis B. (b) Use your answer from part (a) to find the coordinate vector of the vector x = (1,2, –1) relative to the basis B. (c) Find the transition matrix from B to S. (d) Use your answer from part (c) to express the vector x = standard basis S. Give the coordinates for this vector relative to the basis S. (5, 1, 3) in terms of the

Consider the two Dases S 3 {(1,0, 0), (0, 1,0), (0,0, 1)} and в — {(1,0, 1), (0, -1,2), (2, 3, —5)} for R' (Hint: Throughout this problem, refer to section 5 in the notes on Canvas, or the relevant sections in your textbook). (a) Find the transition matrix P 1 from the standard basis S to the nonstandard basis B. (b) Use your answer from part (a) to find the coordinate vector of the vector x = (1,2, –1) relative to the basis B. (c) Find the transition matrix from B to S. (d) Use your answer from part (c) to express the vector x = standard basis S. Give the coordinates for this vector relative to the basis S. (5, 1, 3) in terms of the

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 14EQ

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