OCR FP1 2010 January — Question 1 5 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMatrices
TypeSingular matrix conditions
DifficultyModerate -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.
Spec4.03b 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.
  1. Find A-4I.
  2. Given that \(\mathbf { A }\) is singular, find the value of \(a\).

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]}}