Exercise 1.1.1

Question

Describe geometrically (line, plane, or all of $\mathbf{R}^{3}$) all linear combinations of
$$	ext{(a) } \left[\begin{array}{l}1 \ 2 \ 3\end{array}ight]	ext{ and } \left[\begin{array}{l}3 \ 6 \ 9\end{array}ight]
\qquad 
	ext{(b) } \left[\begin{array}{l}1 \ 0 \ 0\end{array}ight]	ext{ and }\left[\begin{array}{l}0 \ 2 \ 3\end{array}ight]
\qquad
	ext{(c) } \left[\begin{array}{l}2 \ 0 \ 0\end{array}ight]	ext{ and } \left[\begin{array}{l}0 \ 2 \ 2\end{array}ight]	ext{ and } \left[\begin{array}{l}2 \ 2 \ 3\end{array}ight].$$

Prakash Anand · Accepted Answer

The combinations give
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(a) a line in $\mathbf{R}^{3}$
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(b) a plane in $\mathbf{R}^{3}$
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(c) all of $\mathbf{R}^{3}$.

Exercise 1.1.1

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Exercise 1.1.1

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