6 a = \( \begin{pmatrix} 3 \\ 4 \end{pmatrix} \) b = \( \begin{pmatrix} 5 \\ -2 \end{pmatrix} \) Find \( 2a - 3b \) as a column vector. - Edexcel - GCSE Maths - Question 7 - 2020 - Paper 2

To find ( 3b ), we multiply each element of vector ( b ) by 3:

[ 3b = 3 \times \begin{pmatrix} 5 \ -2 \end{pmatrix} = \begin{pmatrix} 3 \times 5 \ 3 \times -2 \end{pmatrix} = \begin{pmatrix} 15 \ -6 \end{pmatrix} ]

Now, we subtract ( 3b ) from ( 2a ):

[ 2a - 3b = \begin{pmatrix} 6 \ 8 \end{pmatrix} - \begin{pmatrix} 15 \ -6 \end{pmatrix} = \begin{pmatrix} 6 - 15 \ 8 - (-6) \end{pmatrix} = \begin{pmatrix} -9 \ 14 \end{pmatrix} ]