1.14 MatricesIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What is the order of a matrix?
When can two matrices be added?
When is AB defined?
If A is m\times n and B is n\times p, what is the order of AB?
Is matrix multiplication commutative?
Is matrix multiplication associative?
What does the identity matrix I do?
Determinant of \begin{pmatrix}a&b\\ c&d\end{pmatrix}?
Inverse of \begin{pmatrix}a&b\\ c&d\end{pmatrix}?
When does a square matrix have no inverse?
How do you solve A\mathbf{x}=\mathbf{b}?
How do you decode a message coded by K?

Exam questions on 1.14 Matrices

$A=\begin{pmatrix}2&1\\ 3&4\end{pmatrix}$ and $B=\begin{pmatrix}1&0\\ -1&2\end{pmatrix}$ .
Find $BA$ and hence state, with a reason, whether $AB=BA$ .2 marks
A cafe sells small cups of coffee at $s$ EUR each and large cups at $l$ EUR each. On Monday, 3 small and 2 large cups cost 13.90 EUR in total. On Tuesday, 2 small and 5 large cups cost 21.00 EUR in total.
Use $\mathbf{x}=A^{-1}\mathbf{b}$ with your GDC, where $A$ is the coefficient matrix, to find the price of a small cup and of a large cup.2 marks
Letters are replaced by numbers ( $A=1$ , $B=2$ , ..., $Z=26$ ) and a message is coded in pairs of letters. Each pair of numbers forms a column vector, which is multiplied on the left by the matrix $K=\begin{pmatrix}2&3\\ 1&2\end{pmatrix}$ to give the coded pair.
Show that $\det K=1$ and find $K^{-1}$ .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).