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Math / Elementary Linear Algebra 8 / Chapter 6.1 / Problem 79

Elementary Linear Algebra | 8th Edition | ISBN: 9781305658004 | Authors: Ron Larson

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Solved: Proof Let S = {v1, v2, . . . , vn} be a set of

Chapter 6, Problem 79

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QUESTION:

Let \(S = {v_{1}, v_{2}, . . . , v_{n}}\) be a set of linearly dependent vectors in V, and let T be a linear transformation from V into V. Prove that the set \({T(v_{1}), T(v_{2}), . . . , T(v_{n})}\) is linearly dependent.

Text Transcription:

S = {v_1, v_2, . . . , v_n}

{T(v_1), T(v_2), . . . , T(v_n)}

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QUESTION:

Let \(S = {v_{1}, v_{2}, . . . , v_{n}}\) be a set of linearly dependent vectors in V, and let T be a linear transformation from V into V. Prove that the set \({T(v_{1}), T(v_{2}), . . . , T(v_{n})}\) is linearly dependent.

Text Transcription:

S = {v_1, v_2, . . . , v_n}

{T(v_1), T(v_2), . . . , T(v_n)}

ANSWER:

Step 1 of 5

Let be a linear transformation and be a linearly dependent set.

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