QUESTION 6 Let T be the linear transformation that takes: 2 and 5 and also 3 and 2 2, and a) Explain why the vectors 2 2 2 form a basis for R4 b) Find bases for both the kernel and the range of this linear transformation. c) Indicate the matrix that would represent T with respect to the standard basis of R4 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.2: The Kernewl And Range Of A Linear Transformation
Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...
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QUESTION 6
Let T be the linear transformation that takes:
2 and
5 and also
3 and
2
a) Explain why the vectors
form a basis for R4
b) Find bases for both the kernel and the range of this linear transformation.
c) Indicate the matrix that would represent T with respect to the standard basis of R4
For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
3222
2322
2232
2223
3 2, and
Transcribed Image Text:QUESTION 6 Let T be the linear transformation that takes: 2 and 5 and also 3 and 2 a) Explain why the vectors form a basis for R4 b) Find bases for both the kernel and the range of this linear transformation. c) Indicate the matrix that would represent T with respect to the standard basis of R4 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). 3222 2322 2232 2223 3 2, and
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