The following vector is linearly dependent upon the solution to the previous problem A. \[\left[ {\begin{array}{*{20}{c}} 8 \\ 9 \\ 3 \end{array}} \right]\] B. \[\left[ {\begin{array}{*{20}{c}} { – 2} \\ { – 17} \\ {30} \end{array}} \right]\] C. \[\left[ {\begin{array}{*{20}{c}} 4 \\ 4 \\ 5 \end{array}} \right]\] D. \[\left[ {\begin{array}{*{20}{c}} {13} \\ 2 \\ { – 3} \end{array}} \right]\]

\]” option2=”\[\left[ {\begin{array}{*{20}{c}} { – 2} \\ { – 17} \\ {30} \end{array}} \right]\]” option3=”\[\left[ {\begin{array}{*{20}{c}} 4 \\ 4 \\ 5 \end{array}} \right]\]” option4=”\[\left[ {\begin{array}{*{20}{c}} {13} \\ 2 \\ { – 3} \end{array}} \right]\]” correct=”option1″]

The correct answer is $\boxed{\text{B}}$.

A vector is said to be linearly dependent upon another vector if it is a scalar multiple of the other vector. In other words, if there exists a scalar $k$ such that $v = ky$, then $v$ is said to be linearly dependent upon $y$.

The solution to the previous problem is $\left[ {\begin{array}{*{20}{c}} {13} \ 2 \ { – 3} \end{array}} \right]$.

We can see that $\left[ {\begin{array}{{20}{c}} { – 2} \ { – 17} \ {30} \end{array}} \right] = -2 \left[ {\begin{array}{{20}{c}} {13} \ 2 \ { – 3} \end{array}} \right]$.

Therefore, $\left[ {\begin{array}{{20}{c}} { – 2} \ { – 17} \ {30} \end{array}} \right]$ is linearly dependent upon $\left[ {\begin{array}{{20}{c}} {13} \ 2 \ { – 3} \end{array}} \right]$.