Question
Asked Sep 19, 2019
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Suppose T: R^3 —> R^3 is a linear transformation and (v1,v2,v3) is a linearly dependent set of vectors in R^3. Prove that {T(v1),T(v2),T(v3)} must also be a linearly dependent set.

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Step 1

To show that the linear transformation T takes linearly dependent sets to linearly dependent sets

Step 2
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Given: 3scalars, a,b,c not all zero,such that an+bv, +c 0; Apply T on both sides,and use linearity of T

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Math

Advanced Math