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Solved: Let S = {v1, v2, v3} be a set of linearly

Chapter 6, Problem 78

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QUESTION:

Let \(S = {v_{1}, v_{2}, v_{3}}\) be a set of linearly independent vectors in \(R^{3}\). Find a linear transformation T from \(R^{3}\) into \(R^{3}\) such that the set \({T(v_{1}), T(v_{2}), T(v_{3})}\) is linearly dependent.

Text Transcription:

S = {v_1, v_2, v_3}

R^3

{T(v_1), T(v_2), T(v_3)}

Questions & Answers

QUESTION:

Let \(S = {v_{1}, v_{2}, v_{3}}\) be a set of linearly independent vectors in \(R^{3}\). Find a linear transformation T from \(R^{3}\) into \(R^{3}\) such that the set \({T(v_{1}), T(v_{2}), T(v_{3})}\) is linearly dependent.

Text Transcription:

S = {v_1, v_2, v_3}

R^3

{T(v_1), T(v_2), T(v_3)}

ANSWER:

Step 1 of 3

Let , then

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