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.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 48E: For the linear transformation T:R2R2 given by A=[abba] find a and b such that T(12,5)=(13,0).
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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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