Question

Show that the vectors u = (1, 2, 0), v = (0, −1, 0), w = (1, −1, 1) are linearly
independent

Answer 1

I think you have to use the wronskian method

Answer 2

Set them all in a 3 x 3 matrix and evaluate for the determinant if it's not equal to 0 then they are linearly independent

Answer 3

\[1\left[\begin{matrix}-1 & 0\\ -1 & 1\end{matrix}\right] -2\left[\begin{matrix}0 & 0 \\ 1 & 1\end{matrix}\right]+ 0 \left[\begin{matrix}0 & -1 \\ 1 & -1\end{matrix}\right]\]

Answer 4

So the third matrix will result to 0 because it's being multiplied by 0 for the first and second you evaluate like this:
1( -1 - 0) -2 (0 - 0) = -1 therefore vectors u, v and w, are linearly independent

Answer 5

With a two by two matrix you solve the determinant by \[\left[\begin{matrix}a & b \\ c & d\end{matrix}\right] = ad - bc = determinant\]

Answer 6

Yeah, I got the det to be -1. This, therefore, because det is non zero (-1) it is linear independent. Is that right yeah?

Answer 7

Yes that's right!

Answer 8

Thanks a million man, appreciate it.

Answer 9

No problem..I'm glad you understand it