Solved: Let x1, x2, and x3 be linearly independent vectors in Rn and let y1 = x2 x1, y2

Chapter 3, Problem 7

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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.

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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,

                                                                

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