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)
∣1−15−39−7−2−6h∣=(9h−42)+(−3h−14)+5(18+18)==6h+1236h+123≠0⇒h≠−20.5\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∣∣1−3−2−19−65−7h∣∣=(9h−42)+(−3h−14)+5(18+18)==6h+1236h+123=0⇒h=−20.5
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