Question

Encontre o valor de k para que (k,0,0),(0,k,0) e (0,0,k) sejam linearmente dependentes

Answer 1

Determinante dos pontos tem que ser nulo

$\\ \left[\begin{array}{ccc}k&0&0\\0&k&0\\0&0&k\end{array}\right] \left\begin{array}{ccc}k&0&\\0&k&\\0&0&\end{array}\right] = 0 \\ \\ \\ k.k.k +0.0.0+0.0.0 - ( 0.k.0 +0.0.k+k.0.0) = 0 \\ \\ k^3 = 0 \\ \\ k = 0$