Further Mathematics 7367: Matrices Topical Past Paper Questions

The matrix M is defined as $$ \mathbf{M}=\left[\begin{array}{ccc}5&2&1\\6&3&2k+3\\2&1&5\end{array}\right] $$ where k is a constant. (a) Given that M is a non-singular matrix, find $ M^{-1} $ in terms of k (b)(c) [5 marks] State any restrictions on the value of k (c) [1 mark] Usin…

A is a non-singular $ 2 \times 2 $ matrix and $ A^{T} $ is the transpose of A Using the result $$ (\mathbf{A}\mathbf{B})^{\mathrm{T}}=\mathbf{B}^{\mathrm{T}}\mathbf{A}^{\mathrm{T}} $$ show that $$ (\mathbf{A}^{-1})^{\mathrm{T}}=(\mathbf{A}^{\mathrm{T}})^{-1} $$ $ (\mathbf{A}^{-1}…

The matrix A represents a reflection in the line y = mx, where m is a constant. $$ {\mathrm{S h o w~t h a t~}}\mathbf{A}=\left({\frac{1}{m^{2}+1}}\right)\left[\begin{matrix}{1-m^{2}}&{2m}\\ {2m}&{m^{2}-1}\\ \end{matrix}\right] $$ You may use the result in the formulae booklet. I…