Neco 2020 Further Mathematics Question 5

Practice essay / theory question 5 from the 2020 Neco Further Mathematics examination. This question covers Matrices and Determinants .

Neco 2020 Further Mathematics Essay / Theory

Topic: Matrices and Determinants

Question 5 NECO • 2020 • FURTHER_MATHEMATICS • essay

A 3 \times 3 matrix \(A\) is given by \(A = \begin{bmatrix} 2 & k & 1 \\ 0 & m & 4 \\ p & 5 & 0 \end{bmatrix}. It is known that \(\det A = 20\). If the element \(k\) is increased by 2 (i.e. replaced by \(k+2\)), the matrix becomes singular. \(\)Determine the values of \(k, m\) and \(p\). Then find the element in the second row, third column of \(A^{-1}\).

( a )

Find the value of \(p\) using the information that the matrix becomes singular when \(k\) is replaced by \(k+2\).

( b )

Using \(\det A = 20\) and the value of \(p\) found in part (a), determine the values of \(k\) and \(m\).

( c )

Find the element in the second row, third column of \(A^{-1}\).

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This is Neco 2020 Further Mathematics Question 5. It is one of the essay questions from the 2020 Neco Further Mathematics examination.

The question covers Matrices and Determinants .

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