Determine whether the vectors 1 3 32 1 11 2 2span R3 Determi

Determine whether the vectors (1, -3, 3),(-2, 1, -1),(-1, -2, 2)span R^3. Determine whether the vectors (1, -1, 1),(1, 1, -1),(-l, -1, -1) span R^3.

Solution

8) As (1,-3,3) + (-2,1,-1) = (-1,-2,2) , these vectors are linearly dependent . So they cant span R³

9) The determinant formed by the three vectors is -4 (not zero). So the three vectors are linearly independent and hence form a basis and span R³