GCSE Mathematics (9-1)
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    1. Work out (4−3)+(−25)\begin{pmatrix}4\\-3\end{pmatrix}+\begin{pmatrix}-2\\5\end{pmatrix}.
    2. Work out (72)−(3−4)\begin{pmatrix}7\\2\end{pmatrix}-\begin{pmatrix}3\\-4\end{pmatrix}.
    3. Work out −3(2−5)-3\begin{pmatrix}2\\-5\end{pmatrix}.
    4. Work out 2(1−3)+(−54)2\begin{pmatrix}1\\-3\end{pmatrix}+\begin{pmatrix}-5\\4\end{pmatrix}.
    5. Work out 3(−24)−2(1−3)3\begin{pmatrix}-2\\4\end{pmatrix}-2\begin{pmatrix}1\\-3\end{pmatrix}.
    6. A route has vector (−42)\begin{pmatrix}-4\\2\end{pmatrix}, followed by (7−6)\begin{pmatrix}7\\-6\end{pmatrix}. Find the total vector.
    7. Find the vector opposite to (−53)\begin{pmatrix}-5\\3\end{pmatrix}.
    8. Given a=(2−1)\mathbf{a}=\begin{pmatrix}2\\-1\end{pmatrix} and b=(−34)\mathbf{b}=\begin{pmatrix}-3\\4\end{pmatrix}, work out 2a−3b2\mathbf{a}-3\mathbf{b}.
    Answers and concise solutions

    1. Vector sum

    Answer: (22)\begin{pmatrix}2\\2\end{pmatrix}.

    2. Vector difference

    Answer: (46)\begin{pmatrix}4\\6\end{pmatrix}.

    3. Scaled vector

    Answer: (−615)\begin{pmatrix}-6\\15\end{pmatrix}.

    4. Combined vector

    Answer: (−3−2)\begin{pmatrix}-3\\-2\end{pmatrix}.

    5. Vector expression

    Answer: (−818)\begin{pmatrix}-8\\18\end{pmatrix}.

    6. Total vector

    Answer: (3−4)\begin{pmatrix}3\\-4\end{pmatrix}.

    7. Opposite vector

    Answer: (5−3)\begin{pmatrix}5\\-3\end{pmatrix}.

    8. Expression value

    Answer: (13−14)\begin{pmatrix}13\\-14\end{pmatrix}.

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