Mathematics 4024 · O Level · Algebraic manipulation

Algebraic manipulation — practice question

The matrices $A = \begin{pmatrix} 1 & 3 \\ -2 & 2 \end{pmatrix}$ and $B = \begin{pmatrix} -1 & 2 \\ -3 & 2 \end{pmatrix}$ are provided.
(a(i))[2]

Find the matrix $2A - B$.

(a(ii))[2]

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

(b)[2]

The matrix $C$ is defined by $3C + 4\begin{pmatrix}-2 & 1 \\ 0 & 3\end{pmatrix} = C$. Find $C$.

(c(i))[2]

For $D = \begin{pmatrix} 3 & 2 \\ 1.5 & 3 \\ 2 & 2.5 \end{pmatrix} \begin{pmatrix} 650 \\ 580 \end{pmatrix}$, find $D$.

(c(ii))[1]

Explain what the information in matrix $D$ means.

(c(iii))[1]

Find the total amount, in dollars, that Theresa receives from selling her fruit.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: $\begin{pmatrix}3 & 4\\-1 & 2\end{pmatrix}$

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