Let T: Rn-->Rm be a linear transformation. a. if T maps Rn onto Rm, give a relationship between m and n. b. if T is one-to-one, give a relationship between m ansd n. c. if T maps Rn onto Rm and is one-to-one, give relationship between m and n

Let T: Rn-->Rm be a linear transformation. a. if T maps Rn onto Rm, give a relationship between m and n. b. if T is one-to-one, give a relationship between m ansd n. c. if T maps Rn onto Rm and is one-to-one, give relationship between m and n

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 4EQ

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Question

Let T: Rⁿ-->R^m be a linear transformation.

a. if T maps Rⁿ onto R^m, give a relationship between m and n.

b. if T is one-to-one, give a relationship between m ansd n.

c. if T maps Rⁿ onto R^m and is one-to-one, give relationship between m and n

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