Gce Model Questions Vol1 2022 Further Mathematics Question 4

Practice objective / multiple choice question 4 from the 2022 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2022 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 4 GCE_MODEL_QUESTIONS_VOL1 • 2022 • FURTHER_MATHEMATICS • objective

Consider the matrix \(M=\begin{pmatrix}2&-1&0\\ k&1&1\\ 0&0&m\end{pmatrix}\) with integers \(k,m\). Suppose \(M\) is invertible and its inverse has only integer entries. (i) Find all possible integer pairs \((k,m)\). (ii) For each pair, state \(\det(M)\).

Answer Options

A. (k,m)=(-1,2), (-1,-1), (-3,2), (-3,-1); det(M)=4 when m=2 and -4 when m=-2
Correct Answer B. (k,m)=(-1,1), (-1,-1), (-3,1), (-3,-1); det(M)=2 when m=1 and -2 when m=-1
C. (k,m)=(-1,1), (-2,1), (-3,1), (-3,-1); det(M)=2 when m=1 and -2 when m=-1
D. (k,m)=(-1,1), (-1,-1), (-2,1), (-2,-1); det(M)=2 when m=1 and -2 when m=-1
Correct Answer
B
Correct Option:
(k,m)=(-1,1), (-1,-1), (-3,1), (-3,-1); det(M)=2 when m=1 and -2 when m=-1

About This Question

This is Gce Model Questions Vol1 2022 Further Mathematics Question 4. It is one of the objective questions from the 2022 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Hard .

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