Question

Determine whether the vectors a=2i-3j+5k,b=3i+j-2k and c=i-7j+12k are linearly dependent or linearly independent

Answer 1

$det\begin{bmatrix} 2 & -3&5 \\ 3 & 1&-2\\ 1&-7&12 \end{bmatrix}=2*1*12+3*5*(-7)+(-3)*(-2)*1-\\- 1*1*5-2*(-7)*(-2)-3*(-3)*12=0.$

So, the vectors are linearly dependent.