Question

Show that {(2,4-2), (3,2,0), (1,-2,2)} does not span R^3

Answer 1

Use elimination.

Answer 2

Elimination is good: i.e., show you can write on of the vectors as the linear combination of the others.

Another method: If these vectors were lin indep they would span R^3. We can test that by evaluating the det of the matrix consisting of these three vectors as the columns (or rows). Call that matrix A

If det(A) = 0, then the vectors are lin dependent. Hence they do not span R^3.

Answer 3

sum of first and third is the second