Heyo, I'm just wondering if I'm correct in assuming that the following three vectors in four dimensional space are linearly dependent.. I simplified them using elemental row operations and ended up with a matrix that has two rows full of zeros, and based on that I concluded that there are infinitely many solutions to the equation system, therefore, the vectors must be dependent. BUT, if you write out the original three vectors as a system of equations, and then calculate the three variables, you come to the conclusion that the only solution is one where all three variables are zero, therefore making the three vectors independent :S a tad confuseddd
$v_1=(1,1,-1,0)^T$
$v_2=(0,-1,1,-2)^T$
$v_3=(3,1,-1,-4)^T$
maany thanks
They are dependent: $$ 3v_1 + 2v_2 - v_3 = 0$$