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Suppose V is a vector space and T : V V is a linear transformation. Suppose v1, v2, v3 V
Chapter 4, Problem 20(choose chapter or problem)
QUESTION:
Suppose V is a vector space and T : V V is a linear transformation. Suppose v1, v2, v3 V are nonzero vectors satisfying T (v1) = v1 T (v2) = 2v2 T (v3) = v3. Prove that {v1, v2, v3} is linearly independent.
Questions & Answers
QUESTION:
Suppose V is a vector space and T : V V is a linear transformation. Suppose v1, v2, v3 V are nonzero vectors satisfying T (v1) = v1 T (v2) = 2v2 T (v3) = v3. Prove that {v1, v2, v3} is linearly independent.
ANSWER:Step 1 of 4
Recall that any linear transformation always preserves the linear independence of vectors