7. Consider the transformation TR4 R4 defined by T(x1, x2, x3, x4) = (x1, x1 + x2, x1 + x2 + x3, x1 + x2 + x3 + x4) (a) Find the associated matrix for T. (b) Find a basis for ker(T). (c) Find a basis for R(T) (Range). (d) Is T one-to-one? Why? (e) Is T onto? Why?
7. Consider the transformation TR4 R4 defined by T(x1, x2, x3, x4) = (x1, x1 + x2, x1 + x2 + x3, x1 + x2 + x3 + x4) (a) Find the associated matrix for T. (b) Find a basis for ker(T). (c) Find a basis for R(T) (Range). (d) Is T one-to-one? Why? (e) Is T onto? Why?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 13E
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