Matrices and Determinants
GCE Further Mathematics

A matrix M is given by M = [[2, 1, -1], [1, 3, 2], [-1, 2, 4]]. (a) Find the determinant of M. [4 marks] (b) Find the matrix of cofactors of M. [6 marks] (c) Hence, find the inverse of M, M⁻¹. [4 mark…

Two matrices P and Q are defined as: P = [[3, k], [2, 5]] and Q = [[1, -2], [0, 4]] where k is a real constant. (a) Find PQ in terms of k. [3 marks] (b) Given that det(PQ) = 46, find the value of k. …

If A = [[3, 1], [2, 4]] and B = [[1, 2], [0, 3]], find AB.

The matrix $A = \begin{pmatrix} k & 2 \\ 3 & k \end{pmatrix}$ is singular. Find the values of k.

Given that $P = \begin{pmatrix} 2 & -1 \\ 4 & 3 \end{pmatrix}$, find the transpose of P, denoted $P^T$.

Given that A = [[2, 3], [1, 4]], find the determinant of A.

If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}$, find $\det(AB)$.

Find the $2 \times 2$ matrix X such that $X\begin{pmatrix} 3 & 1 \\ 5 & 2 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$.

Evaluate the determinant $\begin{vmatrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6 \end{vmatrix}$.

Find the value of x if $\begin{vmatrix} x & 2 \\ 5 & x+1 \end{vmatrix} = 6$.

If M = [[5, 2], [3, 1]], find M⁻¹, the inverse of M.