Verify the identity Ax(BXC) = B(AC) - C(A-B) using the following vectors A = ax + 2ay + 3az B = ax ay + Az C = -ax+ 2ay + az -

The zero vector 0 = (0, 0, 0) can be written a linear combination of the vectors v., v,, and v- because 0 = Ov, + 0v, + 0v3. This is called the trivia! 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)

Find a general set of solution vectors x₂ = - 5x2 X₂ = x₁ + 3x₂

Can it be fit diagonally ?