$$ \mathbf{u}=\left[\begin{array}{r}-2 \ 3\end{array} ight], \mathbf{v}=\left[\begin{array}{r}-6 \ 2\end{array} ight] $$ $$ \mathbf{u}+\mathbf{v}=\square $$ (Simplify your answer.) Compute $$ \mathbf{u}+\mathbf{v} $$ and $$ \mathbf{u}-3 \mathbf{v} $$.

Question

$$ \mathbf{u}=\left[\begin{array}{r}-2 \ 3\end{array}ight], \mathbf{v}=\left[\begin{array}{r}-6 \ 2\end{array}ight] $$ $$ \mathbf{u}+\mathbf{v}=\square $$ (Simplify your answer.) Compute $$ \mathbf{u}+\mathbf{v} $$ and $$ \mathbf{u}-3 \mathbf{v} $$.

UpStudy AI · Accepted Answer

**Step 1. Compute $$ \mathbf{u}+\mathbf{v} $$:**

Given  
$$
\mathbf{u} = \begin{pmatrix} -2 \ 3 \end{pmatrix}, \quad \mathbf{v} = \begin{pmatrix} -6 \ 2 \end{pmatrix},
$$
compute the sum component-wise:
$$
\mathbf{u}+\mathbf{v} = \begin{pmatrix} -2 + (-6) \ 3 + 2 \end{pmatrix} = \begin{pmatrix} -8 \ 5 \end{pmatrix}.
$$

**Step 2. Compute $$ \mathbf{u}-3\mathbf{v} $$:**

First, calculate $$ 3\mathbf{v} $$:
$$
3\mathbf{v} = 3 \begin{pmatrix} -6 \ 2 \end{pmatrix} = \begin{pmatrix} -18 \ 6 \end{pmatrix}.
$$
Then, subtract:
$$
\mathbf{u}-3\mathbf{v} = \begin{pmatrix} -2 \ 3 \end{pmatrix} - \begin{pmatrix} -18 \ 6 \end{pmatrix} = \begin{pmatrix} -2 - (-18) \ 3 - 6 \end{pmatrix} = \begin{pmatrix} 16 \ -3 \end{pmatrix}.
$$

**Final Answers:**
$$
\mathbf{u}+\mathbf{v} = \begin{pmatrix} -8 \ 5 \end{pmatrix}, \quad \mathbf{u}-3\mathbf{v} = \begin{pmatrix} 16 \ -3 \end{pmatrix}.
$$
$$ \mathbf{u}+\mathbf{v} = \begin{pmatrix} -8 \ 5 \end{pmatrix}, \quad \mathbf{u}-3\mathbf{v} = \begin{pmatrix} 16 \ -3 \end{pmatrix} $$

(Simplify your answer.)
Compute and .

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(Simplify your answer.) Compute and .