Answer to Question #316820 in Linear Algebra for danarepo

Question

For what values of h the vectors

⟶              ⟶                 ⟶  

u1 = [1, -3, -2]             u2 = [-1, 9, -6]              u3 = [5, -7, h]   

     

are linearly independent? (Show all working)

Note: The three vectors are supposed to be in a 3x1 matrix(3 rows and 1 column)

Answer 1

$\left| \begin{matrix} 1& -1& 5\\ -3& 9& -7\\ -2& -6& h\\\end{matrix} \right|=\left( 9h-42 \right) +\left( -3h-14 \right) +5\left( 18+18 \right) =\\=6h+123\\6h+123\ne 0\Rightarrow h\ne -20.5$