Matrices and Transformation Topic question [CIE Extended Mathematics (2017-2018)]

 

1	(2018/w/21/q20) \( \mathbf{M}=\left(\begin{array}{ll}8 & 2 \\ 7 & 3\end{array}\right) \quad \mathbf{N}=\left(\begin{array}{rr}4 & -1 \\ -3 & 5\end{array}\right) \) (a)Find $\mathbf{MN}$...[2] (b)Find $\mathbf{M}^{-1}$....[2]
2	(2017/m/22/q18) \( \mathbf{M}=\left(\begin{array}{ll}5 & 3 \\ 1 & -2\end{array}\right) \quad \mathbf{N}=\left(\begin{array}{rr}3 & -6 \\ 4 & 2\end{array}\right) \)  (a)Find $\mathbf{MN}$...[2] (b)Find $\mathbf{M}^{-1}$....[2]
3	(2018/s/22/q20) \( \mathbf{A}=\left(\begin{array}{ll}1 & 1 \\ 9 & 9\end{array}\right) \quad \mathbf{B}=\left(\begin{array}{rr}0 & 1 \\ 9 & 8\end{array}\right) \) \( \mathbf{C}=\left(\begin{array}{ll}1 & 1 \\ 3 & 3\end{array}\right) \quad \mathbf{I}=\left(\begin{array}{rr}1 & 0 \\ 0 & 1\end{array}\right) \)  (a)Here are four matric calculations.  $\mathbf{AI} \quad \mathbf{IA} \quad \mathbf{C^2} \quad \mathbf{B+I}$  Work out which matrix calculation does not give the answer \( \mathbf{M}=\left(\begin{array}{ll}1 & 1 \\ 9 & 9\end{array}\right)\)...[2]  (b) Find $\lvert \mathbf{B} \rvert$...[1]  (c) Explain why Matrix A has no inverse....[1]
4	(2018/w/22/q15) \( \mathbf{M}=\left(\begin{array}{rr}5 & -3 \\ -2 & 1\end{array}\right) \)  (a)Find 3M....[1]  (b)Find M$^{-1}$....[2]
5	(2017/w/23/q19) \( \mathbf{M}=\left(\begin{array}{rr}-2 &  0\\ 5 & -6\end{array}\right) \quad \mathbf{N}=\left(\begin{array}{rr} -3 &  1 \\  0 & -1\end{array}\right) \)  (a) Workout NM....[2]  (b) Find M$^{-1}$, the inverse of M....[2]