If {~v1,··· ,~vr} is linearly independent and T is a one to one linear transformation, show that {T~v1,··· ,T~vr} is also linearly independent. Give an example which shows that if T is only linear, it can happen that, although {~v1,··· ,~vr} is linearly independent, {T~v1,··· ,T~vr} is not
If {~v1,··· ,~vr} is linearly independent and T is a one to one linear transformation, show that {T~v1,··· ,T~vr} is also linearly independent. Give an example which shows that if T is only linear, it can happen that, although {~v1,··· ,~vr} is linearly independent, {T~v1,··· ,T~vr} is not
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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If {~v1,··· ,~vr} is linearly independent and T is a one to one linear transformation, show that {T~v1,··· ,T~vr} is also linearly independent. Give an example which shows that if T is only linear, it can happen that, although {~v1,··· ,~vr} is linearly independent, {T~v1,··· ,T~vr} is not. In fact, show that it can happen that each of the T~vj equals 0.
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