OCR MEI
Further Pure Core AS
2022
June
— Question 1
Exam Board
OCR MEI
Module
Further Pure Core AS (Further Pure Core AS)
Year
2022
Session
June
Topic
Matrices
1
Write the following simultaneous equations as a matrix equation.
$$\begin{aligned}
x + y + 2 z & = 7
2 x - 4 y - 3 z & = - 5
- 5 x + 3 y + 5 z & = 13
\end{aligned}$$
Hence solve the equations.
Determine the set of values of the constant \(k\) for which the matrix equation
$$\left( \begin{array} { c c }
k + 1 & 1
2 & k
\end{array} \right) \binom { x } { y } = \binom { 23 } { - 17 }$$
has a unique solution.