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Solved: Let x1, x2, and x3 be linearly independent vectors in Rn and let y1 = x2 x1, y2
Chapter 3, Problem 7(choose chapter or problem)
QUESTION:
Let x1, x2, and x3 be linearly independent vectors in Rn and let y1 = x2 x1, y2 = x3 x2, y3 = x3 x1 Are y1, y2, and y3 linearly independent? Prove your answer.
Questions & Answers
QUESTION:
Let x1, x2, and x3 be linearly independent vectors in Rn and let y1 = x2 x1, y2 = x3 x2, y3 = x3 x1 Are y1, y2, and y3 linearly independent? Prove your answer.
ANSWER:Step 1 of 2
To prove that, , , and are linearly independent, check when does a linear combination of , , and vanish.
It is given that , , and are linearly independent vectors.
It is observe that,