1.14 MatricesIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 1.14 Matrices

1. $A=\begin{pmatrix}2&1\\ 3&4\end{pmatrix}$ and $B=\begin{pmatrix}1&0\\ -1&2\end{pmatrix}$.
   Find $BA$ and hence state, with a reason, whether $AB=BA$.2 marks
2. 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
3. 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