$$\left(\begin{matrix}1 \ 0 \ 1\end{matrix}\right) \left(\begin{matrix}1 \ 1 \ 0\end{matrix}\right) \left(\begin{matrix}0 \ 1 \ 1\end{matrix}\right)$$

Determine if the vectors do lie in the same plane.

Question

$$\left(\begin{matrix}1 \ 0 \ 1\end{matrix}\right) \left(\begin{matrix}1 \ 1 \ 0\end{matrix}\right) \left(\begin{matrix}0 \ 1 \ 1\end{matrix}\right)$$

Determine if the vectors do lie in the same plane.

phi · Answer

do you know about "reduced row echelon" form ?

if you do, put the matrix formed by those vectors into rref
if you get a row of zeros, then the vectors lie in the same plane... meaning one of the vectors can be written as a linear combination of the other two vectors

anonymous · Answer

should you take a combination of columns or of rows?

phi · Answer

it does not matter here

anonymous · Answer

ok

if I copied the vectors correctly then
I should be able to find a combination of columns

phi · Answer

the 3 vectors are independent

anonymous · Answer

then I copied them wrong :)
thanks!!