Let u and v be vectors in R^n. It can be shown that the set P of all points in the parallelogram determined by u and v has the form au+bv, for 0 ≤ a ≤ 1, 0 ≤ b ≤ 1. Let T : R^n --> R^m be a linear transformation. Explain why the image of a point in T under the transformation T lies in the parallelogram determined by T(u) and T(v).

# Let u and v be vectors in R^n. It can be shown that the set P of all points in the parallelogram determined by u and v has the form au+bv, for 0 ≤ a ≤ 1, 0 ≤ b ≤ 1. Let T : R^n --> R^m be a linear transformation. Explain why the image of a point in T under the transformation T lies in the parallelogram determined by T(u) and T(v).

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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