Gce Model Questions Vol1 2020 Further Mathematics Question 24

Practice objective / multiple choice question 24 from the 2020 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2020 Further Mathematics Objective / Multiple Choice Hard Difficulty

Question 24 GCE_MODEL_QUESTIONS_VOL1 • 2020 • FURTHER_MATHEMATICS • objective

Let \(A = \begin{pmatrix}2 & 1\\ k & 3\end{pmatrix}\) where \(k\) is an integer. (i) Find all integer values of \(k\) for which \(A\) is invertible and its inverse has only integer entries. (ii) For each such \(k\), give \(A^{-1}\).

Answer Options

A. k = 4 with A^{-1}=\begin{pmatrix}3 & -1\\ -4 & 2\end{pmatrix}; k = 6 with A^{-1}=\begin{pmatrix}-3 & 1\\ 6 & -2\end{pmatrix}

B. k = 1 with A^{-1}=\begin{pmatrix}3 & -1\\ -1 & 2\end{pmatrix}; k = 9 with A^{-1}=\begin{pmatrix}-3 & 1\\ 9 & -2\end{pmatrix}

Correct Answer C. k = 5 with A^{-1}=\begin{pmatrix}3 & -1\\ -5 & 2\end{pmatrix}; k = 7 with A^{-1}=\begin{pmatrix}-3 & 1\\ 7 & -2\end{pmatrix}

D. k = 5 with A^{-1}=\begin{pmatrix}2 & -1\\ -5 & 3\end{pmatrix}; k = 8 with A^{-1}=\begin{pmatrix}-2 & 1\\ 8 & -3\end{pmatrix}

Correct Answer

Correct Option:

k = 5 with A^{-1}=\begin{pmatrix}3 & -1\\ -5 & 2\end{pmatrix}; k = 7 with A^{-1}=\begin{pmatrix}-3 & 1\\ 7 & -2\end{pmatrix}

About This Question

This is Gce Model Questions Vol1 2020 Further Mathematics Question 24. It is one of the objective questions from the 2020 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Hard .

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