Let T : R4 →R2 be a linear transformation, and let A be the standard matrix of T . Assume that no two columns of A are parallel. a. How many rows and how many columns must A have? b. Is T 1-1? Explain. c. Is T onto? Explain.

Let T : R4 →R2 be a linear transformation, and let A be the standard matrix of T . Assume that no two columns of A are parallel. a. How many rows and how many columns must A have? b. Is T 1-1? Explain. c. Is T onto? Explain.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter10: Matrices

Section10.CR: Chapter 10 Review

Problem 15CR

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Question

Let T : R⁴ →R² be a linear transformation, and let A be the standard matrix of T . Assume that no two columns of A are parallel.

a. How many rows and how many columns must A have?

b. Is T 1-1? Explain.

c. Is T onto? Explain.

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