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Solved: In Exercises, use determinants to decide if the
Chapter 3, Problem 26E(choose chapter or problem)
In Exercises 24–26, use determinants to decide if the set of vectors is linearly independent.
\(\left[\begin{array}{r}3 \\ 5 \\ -6 \\ 4\end{array}\right],\left[\begin{array}{r}2 \\ -6 \\ 0 \\ 7\end{array}\right],\left[\begin{array}{r}-2 \\ -1 \\ 3 \\ 0\end{array}\right],\left[\begin{array}{r}0 \\ 0 \\ 0 \\ -2\end{array}\right]\)
Questions & Answers
QUESTION:
In Exercises 24–26, use determinants to decide if the set of vectors is linearly independent.
\(\left[\begin{array}{r}3 \\ 5 \\ -6 \\ 4\end{array}\right],\left[\begin{array}{r}2 \\ -6 \\ 0 \\ 7\end{array}\right],\left[\begin{array}{r}-2 \\ -1 \\ 3 \\ 0\end{array}\right],\left[\begin{array}{r}0 \\ 0 \\ 0 \\ -2\end{array}\right]\)
ANSWER:Solution:
Step 1
In this problem we need to find out if the set of vectors is linearly independent by using determinant. We will find the determinant of the matrix corresponding to the set of the vectors.