The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v1, v2, and v3 because 0 = 0v1 + 0v2 + 0v3. 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 v1, v2, and v3. if not possible, enter impossible.) v1 = (1, 0, 1), v2 = (−1, 1, 2), v3 = (0, 3, 8)

Step-by-step explanation:

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

We have to find another way without non zero coefficients using v1, v2 and v3

Let us assume a,b,c are non zero coefficients.

Simplifying we have a=b

So II and III equation becomes

The determinant is

1   3

3   8   which is not having value 0

Hence there cannot be any solution other than trivial.

i.e. impossible is answer.

for the free

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