Mathematics 4024 · O Level · Algebraic manipulation

Algebraic manipulation — practice question

$A=\begin{pmatrix}2&0\\3&1\end{pmatrix}$ together with $B=\begin{pmatrix}1&2\\-1&3\end{pmatrix}$.
(a)[2]

Find the value of $A+2B$.

(b)[2]

Find the product $AB$.

(c)[2]

If $A\begin{pmatrix}x\\2\end{pmatrix}=\begin{pmatrix}8\\2y\end{pmatrix}$, find the values of $x$ and $y$.

(d)[2]

Find the inverse matrix $B^{-1}$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: The matrix is $\begin{pmatrix}4 & 4\\1 & 7\end{pmatrix}$.

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