Let $H$ be the set of all vectors of the form $egin{bmatrix} s \ 3s \ 2s end{bmatrix}$. Find a vector $v$ in $mathbb{R}^3$ such that $H = ext{Span}{v}$. Why does this show that $H$ is a subspace of $mathbb{R}^3$?
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The vectors in \( H \) are of the form: \[ \begin{bmatrix} s \\ 3s \\ 2s \end{bmatrix} \] Step 2: Express the vector in \( H \) in terms of a scalar multiple. Notice that: \[ \begin{bmatrix} s \\ 3s \\ 2s \end{bmatrix} = s \begin{bmatrix} 1 \\ 3 \\ 2 Show more…
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