Question

determine whether the following are linearly indepent or not alpha=(1,-1,0) ; beta=(1,3,-1) ; …

Answer 1

Can you find a constant c such that
c <1,-1,0> = <1,3,-1>
?

Answer 2

yes

Answer 3

not likely you can, since \(c0=0\) and never \(-1\)

Answer 4

\[\alpha=(1;-1;0) ;\beta=(1;3;-1) ;\gamma=(5;3;2)\]
determine whether it is linearly independent

Answer 5

\[\begin{bmatrix} 1 & 1 & 5 \\ -1 & 3 & 3 \\ 0 & -1 & 2 \end{bmatrix}\]

Answer 6

What is the determinant of this matrix? What follows if it's non-zero?