The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v., v, and v because 0 = Ov, + 0v2 + Ov3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v. If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6) 0 =

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A: We can write the answer in the below steps.

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A: The solution is given as

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A: See the attachment

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A: Given that (0,0,0) = 0v1+0v2+0v3 is one way of writing in a trivial way the vector 0.

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A: Use Cross product of vector

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Q: Hi, any help on this problem would be greatly appreciated. Thank you!

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A: The solution of the problem is given in the next steps.

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v,, v,, and v,…

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