Further Pure Mathematics WFM01: MATRIX ALGEBRA Topical Past Paper Questions

The matrix M is given by $$ \begin{pmatrix}{-2}&{2}&{2} \\{-3}&{-7}&{-3} \\{1}&{1}&{-3}\end{pmatrix} $$ (a) Show that $ \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix} $ is an eigenvector of M, stating the corresponding eigenvalue. [3] (b) Show that the eigenvalue from part (a) is the…

$$ \mathbf{A}=\begin{pmatrix}1&k&2\\5&3&-2\\6&-1&4\end{pmatrix} $$ where k is a constant (a) Determine the value of k for which A is singular. (3) Given that A is non-singular, (b) determine $ A^{-1} $, giving your answer in simplest form in terms of k. (4)

$$ \mathbf{M}=\begin{pmatrix}{{{2}}}&{{{0}}}&{{{3}}} \\{{{0}}}&{{{-4}}}&{{{-3}}} \\{{{0}}}&{{{-4}}}&{{{0}}}\end{pmatrix} $$ Given that M has exactly two distinct eigenvalues $ \lambda_{1} $ and $ \lambda_{2} $, where $ \lambda_{1} (6) ( The line $ l_{1} $ has equation $ \mathbf{r…