MatricesIB MYP Maths Extended: Mind map

Exam questions on Matrices

1. The matrices $\mathbf A$ and $\mathbf B$ are given by $\mathbf A=\begin{pmatrix}2&-1\\ 0&3\end{pmatrix}$ and $\mathbf B=\begin{pmatrix}1&4\\ -2&5\end{pmatrix}$.
   Find $\mathbf A^2$.2 marks
2. $\mathbf M=\begin{pmatrix}1&2&3\\ 4&0&1\end{pmatrix}$ and $\mathbf N=\begin{pmatrix}2&1\\ 0&3\\ 1&-1\end{pmatrix}$.
   Find the matrix $\mathbf{MN}$.2 marks
3. Four towns $W$, $X$, $Y$ and $Z$ are joined by two-way bus routes. The only direct routes are $W$ to $X$, $W$ to $Y$, $X$ to $Y$, and $Y$ to $Z$.
   Write down the adjacency matrix $\mathbf M$ for the network, using the order $W$, $X$, $Y$, $Z$ for the rows and columns, and state its order.3 marks