Mathematics A, Further H235: Matrices Topical Past Paper Questions

Three transformations, $ T_{A} $, $ T_{B} $ and $ T_{C} $, are represented by the matrices A, B and C respectively. You are given that $ \mathbf{A} = \begin{pmatrix} 1 & 0 \\ 2 & 3 \end{pmatrix} $ and $ \mathbf{B} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} $. (a) Find the ma…

Matrix $\mathbf{R}$ is given by $\mathbf{R}=\begin{pmatrix}a&0&-b\\0&1&0\\b&0&a\end{pmatrix}$ where $a$ and $b$ are constants. (a) Find $\mathbf{R}^{2}$ in terms of $a$ and $b$. [2] The constants $a$ and $b$ are given by $a=\frac{\sqrt{2}}{4}(\sqrt{3}+1)$ and $b=\frac{\sqrt{2}}{4…

The matrix A is given by $ A = \begin{pmatrix} t-1 & t-1 & t-1 \\ 1-t & 6 & t \\ 2-2t & 2-2t & 1 \end{pmatrix} $. (a) Find, in fully factorised form, an expression for det A in terms of t. [3] (b) State the values of t for which A is singular. [1] You are given the following syst…