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(a) Let u and v be (fixed, but unknown) vectors in IR". Suppose that T: RT →R" is a linear transformation such that T(u)=6u+v and T(v) = 4u - 2v. Compute (ToT)(v), where To T is the composition of T with itself. Express your answer as a linear combination of u and v. (TT)(v) 12 u 13 v (b) Let v and w be (fixed, but unknown) vectors in IR", which are not scalar multiples of each others. Suppose that T: RT → R is a linear transformation such that Compute T(v) and express it as a linear combination of v and w. T(v) = v + W T(4v+3w)=3v+2w and T(v+1w) = 5v+3w.

(a) Let u and v be (fixed, but unknown) vectors in IR". Suppose that T: RT →R" is a linear transformation such that T(u)=6u+v and T(v) = 4u - 2v. Compute (ToT)(v), where To T is the composition of T with itself. Express your answer as a linear combination of u and v. (TT)(v) 12 u 13 v (b) Let v and w be (fixed, but unknown) vectors in IR", which are not scalar multiples of each others. Suppose that T: RT → R is a linear transformation such that Compute T(v) and express it as a linear combination of v and w. T(v) = v + W T(4v+3w)=3v+2w and T(v+1w) = 5v+3w.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.CR: Review Exercises
Problem 21CR: Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find...
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(a) Let u and v be (fixed, but unknown) vectors in IR". Suppose that T: RT →R" is a linear transformation such that T(u)=6u+v and T(v) = 4u - 2v. Compute (ToT)(v), where To T is the composition of T with itself. Express your answer as a linear combination of u and v. (TT)(v) 12 u 13 v (b) Let v and w be (fixed, but unknown) vectors in IR", which are not scalar multiples of each others. Suppose that T: RT → R is a linear transformation such that Compute T(v) and express it as a linear combination of v and w. T(v) = v + W T(4v+3w)=3v+2w and T(v+1w) = 5v+3w.
Transcribed Image Text:(a) Let u and v be (fixed, but unknown) vectors in IR". Suppose that T: RT →R" is a linear transformation such that T(u)=6u+v and T(v) = 4u - 2v. Compute (ToT)(v), where To T is the composition of T with itself. Express your answer as a linear combination of u and v. (TT)(v) 12 u 13 v (b) Let v and w be (fixed, but unknown) vectors in IR", which are not scalar multiples of each others. Suppose that T: RT → R is a linear transformation such that Compute T(v) and express it as a linear combination of v and w. T(v) = v + W T(4v+3w)=3v+2w and T(v+1w) = 5v+3w.
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