Vectors and Matrices I

Add componentwise: $4 + 2 = 6$ and $-1 + 6 = 5$.

Rows first, columns second. There are three rows and two columns.

$\sqrt{25 + 144} = \sqrt{169} = 13$. Squaring removes the minus sign, so the magnitude is positive.

Multiply both components by $-2$: $-2 \times 3 = -6$ and $-2 \times -2 = 4$. The result is parallel to $\mathbf{a}$ but points the opposite way.

$\overrightarrow{PQ} = \begin{pmatrix} 7 \\ 11 \end{pmatrix} - \begin{pmatrix} 2 \\ -1 \end{pmatrix} = \begin{pmatrix} 5 \\ 12 \end{pmatrix}$, and $\sqrt{25+144} = 13$.

The inner numbers (3 and 3) match, so the multiplication is possible, and the outer numbers give the order of the answer.