Further Mathematics 7366: Matrices Topical Past Paper Questions

The matrix M represents the transformation T, and is given by (a) $$ \mathbf{M}=\left[\begin{array}{cc}3&-1\\ &\\ -2&6\end{array}\right] $$ The point $A$ has coordinates $(4, -5)$ Find the coordinates of the image of A under T [2 marks] (b)(q)(a) Show that the only invariant poin…

The matrix M represents the transformation T and is given by $$ \mathbb{M}=\left[\begin{matrix}{3p+1}&{12}\\ {p+2}&{p^{2}-3}\\ \end{matrix}\right] $$ In the case when $p = 0$ show that the image of the point (4, 5) under T is the point (64, -7) [2 marks] In the case when $ p = -2…

The matrix A is given by $$ \mathbf{A}=\begin{bmatrix}{{{5}}}&{{{2}}} \\{{{-3}}}&{{{4}}}\end{bmatrix} $$ (a) Find det A Find det A [1 mark] (b) Find $ \mathbf{A}^{-1} $ Find $ A^{-1} $ [1 mark] (c) Given that $ AB = \begin{bmatrix} 9 & 6 \\ 5 & 12 \end{bmatrix} $ and $ M = 2A + B…