Question

In Exercises10through 20 , use paper and pencil to identify the redundant vectors. Thus determine whether the given vectors are linearly independent.

13.$\left[\begin{array}{c}1\\ 2\end{array}\right],\mathbf{\left[}\begin{array}{c}\mathbf{1}\\ \mathbf{2}\end{array}\mathbf{\right]}$ .

Short answer

The vectors $\left[\begin{array}{c}1\\ 2\end{array}\right],\left[\begin{array}{c}1\\ 2\end{array}\right]$are redundant and linearly dependent.

Step-by-step solution

Consider the set.

The vectors ${\overrightarrow{v}}_1,{\overrightarrow{v}}_2,...,{\overrightarrow{v}}_m$in ${\mathrm{ℝ}}^n$are linearly dependent if and only if there are nontrivial relation among them.

If linearly dependent, then, the vectors are said to be redundant.

Consider the vectors,$\left[\begin{array}{c}1\\ 2\end{array}\right],\left[\begin{array}{c}1\\ 2\end{array}\right]$

Check for linear independency of vectors.

The vectors are.

$V_1=\left[\left.\begin{array}{c}1\\ 2\end{array}\right],V_2=\left[\begin{array}{c}1\\ 2\end{array}\right.\right]$

$V_2=V_1$

Final answer.

The vectors $\left[\begin{array}{c}1\\ 2\end{array}\right]\left[\begin{array}{c}1\\ 2\end{array}\right]$are redundant and linearly dependent.