÷ÈÓ°Ö±²¥

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

10.$\left[\begin{array}{c}7\\ 11\end{array}\right]\left[\begin{array}{c}0\\ 0\end{array}\right]$.

The column vectors of a 5×4 matrix must be linearly dependent.

In Exercises 10 through 20 , use paper and pencil to identify the redundant vectors. Thus determine whether the given vectors are linearly independent.

11.$\mathbf{\left[}\begin{array}{c}\mathbf{7}\\ \mathbf{11}\end{array}\mathbf{\right]}\mathbf{,}\mathbf{\left[}\begin{array}{c}\mathbf{11}\\ \mathbf{7}\end{array}\mathbf{\right]}$ .

If matrix A is similar to matrix B, and matrix B is similar to matrix C, then C must be similar to matrix A.

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

12.$\left[\begin{array}{c}2\\ 1\end{array}\right]\mathbf{,}\left[\begin{array}{c}6\\ 3\end{array}\right]$ .

If a subspace V of $R^n$contains none of the standard vectors $e_1,e_2,...e_n$ then V consists of the zero vector only.

If vectors ${\stackrel{→}{v}}_1,{\stackrel{→}{v}}_2,{\stackrel{→}{v}}_{3}and\stackrel{→}{v_4}$are linearly independent, then vectors ${\stackrel{→}{v}}_1,{\stackrel{→}{v}}_2,{\stackrel{→}{v}}_3$ must be linearly independent as well.

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

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

The vectors of the form $\left[\begin{array}{c}\mathit{a}\\ \mathit{b}\\ 0\\ \mathit{a}\end{array}\right]$(where a and b are arbitrary real numbers) forms a subspace of$R^4.$

In Exercises 10 through 20 , use paper and pencil to identify the redundant vectors. Thus determine whether the given vectors are linearly independent.

14.$\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]\mathbf{,}\left[\begin{array}{c}3\\ 2\\ 1\end{array}\right]\mathbf{,}\left[\begin{array}{c}6\\ 5\\ 4\end{array}\right]$ .