Solution Found!
Answer: Find the value(s) of h for which the vectors are
Chapter 1, Problem 12E(choose chapter or problem)
Find the value(s) of h for which the vectors are linearly dependent. Justify each answer.
\(\left[\begin{array}{r}2 \\ -4 \\ 1\end{array}\right],\left[\begin{array}{r}-6 \\ 7 \\ -3\end{array}\right],\left[\begin{array}{l}8 \\ h \\ 4\end{array}\right]\)
Questions & Answers
QUESTION:
Find the value(s) of h for which the vectors are linearly dependent. Justify each answer.
\(\left[\begin{array}{r}2 \\ -4 \\ 1\end{array}\right],\left[\begin{array}{r}-6 \\ 7 \\ -3\end{array}\right],\left[\begin{array}{l}8 \\ h \\ 4\end{array}\right]\)
ANSWER:Solution
Step 1
In this problem we need to find the value of h for which the vectors are linearly dependent.
Given:
Linearly Dependent: The set is said to be linearly dependent if there exists scalars not all zero, such that
Let
Given that the vectors are linearly dependent.
Therefore there exists scalars not all zero, such that
Thus