Let A = {4 -2 5}, let B = {16 -14 22}, let C = {-4 5 -6}? Determine whether or n

Question

Let A = {4 -2 5}, let B = {16 -14 22}, let C = {-4 5 -6}?
Determine whether or not the three vectors listed above are linearly independent or linearly dependent.

The vectors were written horizontally this time, as they often are in books, but that is just to save space. The problem is the same as if the vectors were written vertically.
If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds.

? A + ? B + ? C = 0

Explanation / Answer

a(4i-2j+5k)+b(16i-14j+22k)+c(-4i+5j-6k) = 0

(4a+16b-4c) i +j(-2a-14b+5c)+c(5a+22b-6c)k = 0

4a+16b-4c = 0

-2a-14b+5c = 0

5a+22b-6c = 0

no soln

they are independant

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