Math Solutions

[Solution Library] Let \overrightarrowv_1=[l0 , 0 , 0], \overrightarrowv_2=[l1 , 2 , 3], \overrightarrowv_3=[l1 , 2 , 3], and \overrightarrowv_4=[l2 , 2 , 3].

Question: Let $\overrightarrow{v_{1}}=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right], \overrightarrow{v_{2}}=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right], \overrightarrow{v_{3}}=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, and $\overrightarrow{v_{4}}=\left[\begin{array}{l}2 \\ 2 \\ 3\end{array}\right]$.

$[10 \mathrm{marks}]$

How many vectors are in $\left\{\vec{v}_{1}\right\} ?$ How many vectors are in $\operatorname{span}\left\{\vec{v}_{1}\right\} ?$ What is $\operatorname{dim} \operatorname{span}\left\{\vec{v}_{1}\right\} ?$
How many vectors are in $\left\{\overrightarrow{v_{1}}, \overrightarrow{v_{2}}\right\}$ ? How many vectors are in $\operatorname{span}\left\{\overrightarrow{v_{1}}, \overrightarrow{v_{2}}\right\}$ ? What is $\operatorname{dim} \operatorname{span}\left\{\overrightarrow{v_{1}}, \overrightarrow{v_{2}}\right\} ?$
How many vectors are in $\left\{\overrightarrow{v_{1}}, \overrightarrow{v_{2}}, \overrightarrow{v_{3}}\right\} ?$ How many vectors are in $\operatorname{span}\left\{\vec{v}_{1}, \dot{\vec{v}_{2}}, \vec{v}_{3}\right\} ?$ What is $\operatorname{dimspan}\left\{\overrightarrow{v_{1}}, \overrightarrow{v_{2}}, \overrightarrow{v_{3}}\right\} ?$
How many vectors are in $\left\{\vec{v}_{1}, \overrightarrow{v_{2}}, \overrightarrow{v_{3}}, \overrightarrow{v_{4}}\right\} ?$ How many vectors are in $\operatorname{span}\left\{\overrightarrow{v_{1}}, \overrightarrow{\vec{v}_{2}}, \overrightarrow{v_{3}}, \overrightarrow{v_{4}}\right\} ?$ What is $\operatorname{dimspan}\left\{\overrightarrow{v_{1}}, \overrightarrow{v_{2}}, \overrightarrow{v_{3}}, \overrightarrow{v_{4}}\right\} ?$

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[Solution Library] Let \overrightarrowv_1=[l0 , 0 , 0], \overrightarrowv_2=[l1 , 2 , 3], \overrightarrowv_3=[l1 , 2 , 3], and \overrightarrowv_4=[l2 , 2 , 3].

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