Solve the problem.
-For what values of h are the given vectors linearly independent? $$\left[ \begin{array} { c }
- 5 \
- 6 \
5
\end{array} \right] , \left[ \begin{array} { c }
20 \
24 \
h
\end{array} \right]$$
A) Vectors are linearly independent for $h \neq - 20$
B) Vectors are linearly independent for all $h$
C) Vectors are linearly dependent for all $h$
D) Vectors are linearly independent for $h = - 20$

Question

Solve the problem.
-For what values of h are the given vectors linearly independent? $$\left[ \begin{array} { c } 
- 5 \
- 6 \
5
\end{array} \right] , \left[ \begin{array} { c } 
20 \
24 \
h
\end{array} \right]$$
A) Vectors are linearly independent for $h \neq - 20$
B) Vectors are linearly independent for all $h$
C) Vectors are linearly dependent for all $h$
D) Vectors are linearly independent for $h = - 20$

Quizplus · Accepted Answer

Two vectors are linearly independent if no scalar multiple of one vector equals the other. The second vector is -4 times the first in the first two components. For them to be linearly independent, the third component of the second vector should not be -4 times the third component of the first vector, i.e., $h \neq -4 \times 5 = -20$.

Solve the Problem [−5−65],[2024h]\left[ \begin{array} { c } - 5 \\- 6 \\5\end{array} \right] , \left[ \begin{array} { c } 20 \\24 \\h\end{array} \right]​−5−65​​,​2024h​​

Solve the Problem $\left[ \begin{array} { c } - 5 \\- 6 \\5\end{array} \right] , \left[ \begin{array} { c } 20 \\24 \\h\end{array} \right]$