Question

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)

Answer 1

Answer:

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.

$(0,0,0)=a(1,0,1)+b(-1,1,2) +c(0,3,8)\\a-b=0\\b+3c=0\\a+2b+8c=0$

Simplifying we have a=b

So II and III equation becomes

$b+3c=0\\3b+8c=0$

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.