Question 1
2 marks\(\mathbf{p} = \begin{pmatrix}2\\-4\end{pmatrix}\) and \(\mathbf{q} = \begin{pmatrix}-1\\5\end{pmatrix}\)
Kim works out \(3\mathbf{p} - \mathbf{q}\). Here is her working.
\[3\mathbf{p} - \mathbf{q} = \begin{pmatrix}6\\-12\end{pmatrix} - \begin{pmatrix}-1\\5\end{pmatrix} = \begin{pmatrix}5\\-17\end{pmatrix}\]
Kim's answer is wrong.
Describe the mistake Kim has made and work out the correct answer.
Model answer
Kim has made a mistake with the top numbers: she worked out 6 − 1 = 5, but it should be 6 − (−1) = 6 + 1 = 7.
The bottom number is correct: −12 − 5 = −17.
\(3\mathbf{p} - \mathbf{q} = \begin{pmatrix}7\\-17\end{pmatrix}\)
Explanation
When you subtract a column vector, subtract each component separately and take care with negative numbers. Subtracting a negative number is the same as adding, so 6 − (−1) = 7.
Mark scheme
-
1 mark
C1 for explaining the error in the top component: she has worked out 6 − 1 instead of 6 − (−1)
oe, e.g. 'she subtracted 1 instead of adding 1', 'subtracting −1 means adding 1'
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1 mark
B1 for \(\begin{pmatrix}7\\-17\end{pmatrix}\)
cao
