Edexcel IGCSE Math B 5 Matrices Questions

The points with coordinates (1,2),(1,5) and (3,2) are the vertices of triangle A.

Find the matrix product $\mathbf{M}\left(\begin{array}{lll}1 & 1 & 3 \\ 2 & 5 & 2\end{array}\right)$

$$A=\begin{pmatrix}2&-3\\4&1\end{pmatrix}, \qquad B=\begin{pmatrix}5&0\\4&-2\end{pmatrix}.$$
Calculate

$$\mathbf A=\begin{pmatrix}2k^2&k-9\\-3k&k+1\end{pmatrix}, \qquad \mathbf B=\begin{pmatrix}1&-5\\3&k\end{pmatrix}.$$
The determinant of matrix $\mathbf A$ is equal to the determinant of matrix $\mathbf B$.

$$A=\begin{pmatrix}2&-3\\4&1\end{pmatrix}, \qquad B=\begin{pmatrix}5&0\\4&-2\end{pmatrix}.$$
Calculate

2A-4B

$$\mathbf A=\begin{pmatrix}2k^2&k-9\\-3k&k+1\end{pmatrix}, \qquad \mathbf B=\begin{pmatrix}1&-5\\3&k\end{pmatrix}.$$
The determinant of matrix $\mathbf A$ is equal to the determinant of matrix $\mathbf B$.

Show that k is a root of the equation
$$2k^3+5k^2-28k-15=0.$$

The vertices of triangle A are the points with coordinates (2,2),(3,2) and (2,4).

Triangle A is transformed to triangle B under the transformation with matrix
$$P=\begin{pmatrix}-2&0\\0&-2\end{pmatrix}.$$

On the grid, draw and label triangle B.

$$\mathbf A=\begin{pmatrix}2k^2&k-9\\-3k&k+1\end{pmatrix}, \qquad \mathbf B=\begin{pmatrix}1&-5\\3&k\end{pmatrix}.$$
The determinant of matrix $\mathbf A$ is equal to the determinant of matrix $\mathbf B$.

The transformation with matrix $\mathbf C$, where $\mathbf C$ is a $2\times2$ matrix, is equivalent to the transformation with matrix $\mathbf A$ followed by the transformation with matrix $\mathbf B$.
Given that k is positive, find matrix $\mathbf C$.

$$\text{Determinant of matrix }\begin{pmatrix}a&b\\c&d\end{pmatrix}=ad-bc.$$