| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Singular matrix conditions |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic matrix operations and the definition of a singular matrix (determinant = 0). Part (i) requires simple matrix subtraction, and part (ii) involves setting det(A) = 4a - 6 = 0 and solving for a. Both parts are routine recall and application of standard definitions with minimal problem-solving required. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03l Singular/non-singular matrices |
1 The matrix $\mathbf { A }$ is given by $\mathbf { A } = \left( \begin{array} { l l } a & 2 \\ 3 & 4 \end{array} \right)$ and $\mathbf { I }$ is the $2 \times 2$ identity matrix.\\
(i) Find A-4I.\\
(ii) Given that $\mathbf { A }$ is singular, find the value of $a$.
\hfill \mbox{\textit{OCR FP1 2010 Q1 [5]}}