| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Conditions for unique solution |
| Difficulty | Moderate -0.8 This is a straightforward question testing basic matrix concepts: converting matrix equations to simultaneous equations and calculating a 2×2 determinant. The interpretation of zero determinant (no unique solution) is standard bookwork. While it's Further Maths content, these are foundational skills with minimal problem-solving required. |
| Spec | 4.03h Determinant 2x2: calculation4.03l Singular/non-singular matrices4.03r Solve simultaneous equations: using inverse matrix |
| Answer | Marks |
|---|---|
| \(6x - 2y = a\) | B1 |
| \(-3x + y = b\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\det = (6)(1) - (-2)(-3) = 6 - 6 = 0\) | M1 A1 | |
| The determinant is zero, so the matrix is singular and the equations do not have a unique solution — either no solution or infinitely many solutions | A1 | must relate to equations |
# Question 4:
**(i)**
$6x - 2y = a$ | B1 |
$-3x + y = b$ | B1 |
**(ii)**
$\det = (6)(1) - (-2)(-3) = 6 - 6 = 0$ | M1 A1 |
The determinant is zero, so the matrix is singular and the equations do not have a unique solution — either no solution or infinitely many solutions | A1 | must relate to equations
---4 The matrix equation $\left( \begin{array} { r r } 6 & - 2 \\ - 3 & 1 \end{array} \right) \binom { x } { y } = \binom { a } { b }$ represents two simultaneous linear equations in $x$ and $y$.\\
(i) Write down the two equations.\\
(ii) Evaluate the determinant of $\left( \begin{array} { r r } 6 & - 2 \\ - 3 & 1 \end{array} \right)$.
What does this value tell you about the solution of the equations in part (i)?
\hfill \mbox{\textit{OCR MEI FP1 2006 Q4 [5]}}