Neco 2023 Further Mathematics Question 5

Practice essay / theory question 5 from the 2023 Neco Further Mathematics examination. This question covers Matrices, Determinants .

Neco 2023 Further Mathematics Essay / Theory

Topics: Matrices Determinants

Question 5 NECO • 2023 • FURTHER_MATHEMATICS • essay

A 2\times2 matrix \(A\) is defined by \(A = \begin{pmatrix} a & 2 \\ 3 & b \end{pmatrix}\) where \(a\) and \(b\) are integers. It is given that \(A^{2}=kA\) for some constant \(k\).

( a )

Find the relationship between \(a\) and \(b\) and determine the value of \(k\).

( b )

Given that \(a\) and \(b\) are positive integers, list all ordered pairs \((a,b)\) that satisfy the relationship found in part (a).

( c )

For each ordered pair found in part (b), state whether \(A\) is invertible. If it is invertible, write down its inverse matrix.

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This is Neco 2023 Further Mathematics Question 5. It is one of the essay questions from the 2023 Neco Further Mathematics examination.

The question covers Matrices, Determinants .

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