MatricesIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

How do you write the order of a matrix?
What is the order of \begin{pmatrix}1&2&3\\ 4&5&6\end{pmatrix}?
When can you add two matrices?
How do you multiply a matrix by a scalar?
When does \mathbf{AB} exist?
\mathbf A is m\times n and \mathbf B is n\times p. Order of \mathbf{AB}?
How do you find an entry of a product?
Is \mathbf{AB}=\mathbf{BA} always?
\begin{pmatrix}1&2\\ 3&4\end{pmatrix}\begin{pmatrix}5\\ 6\end{pmatrix}=?
What does an adjacency matrix show?
What is special about the adjacency matrix of a two-way network?
What do the entries of \mathbf M^2 show?
Entry from Y to Y in \mathbf M^2 with row Y=(1,1,0,1)?

Exam questions on Matrices

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
$\mathbf M=\begin{pmatrix}1&2&3\\ 4&0&1\end{pmatrix}$ and $\mathbf N=\begin{pmatrix}2&1\\ 0&3\\ 1&-1\end{pmatrix}$ .
Find the matrix $\mathbf{MN}$ .2 marks
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).