Neco 2019 Further Mathematics Question 13

Practice objective / multiple choice question 13 from the 2019 Neco Further Mathematics examination.

Neco 2019 Further Mathematics Objective / Multiple Choice Medium Difficulty

Question 13 NECO • 2019 • FURTHER_MATHEMATICS • objective

Consider the matrix \(M=\begin{pmatrix}2& p&1\\4&5& q\\6&7&8\end{pmatrix}\). Find the relationship between \(p\) and \(q\) that makes \(\det M =0\). For any such pair \((p,q)\), determine the rank of \(M\).

A. q = \\frac{32p-78}{6p-12}\\;(p\\neq\\tfrac{2}{1}),\\; \\operatorname{rank}(M)=2

B. q = \\frac{30p-78}{6p-14}\\;(p\\neq\\tfrac{7}{3}),\\; \\operatorname{rank}(M)=2

C. q = \\frac{32p-78}{6p-14}\\;(p\\neq\\tfrac{7}{3}),\\; \\operatorname{rank}(M)=3

Correct Answer D. q = \frac{32p-78}{6p-14}\;(p\neq\tfrac{7}{3}),\; \operatorname{rank}(M)=2

Correct Answer

Correct Option:

q = \frac{32p-78}{6p-14}\;(p\neq\tfrac{7}{3}),\; \operatorname{rank}(M)=2

This is Neco 2019 Further Mathematics Question 13. It is one of the objective questions from the 2019 Neco Further Mathematics examination.

Difficulty level: Medium .

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