Neco 2022 Further Mathematics Question 5
Practice essay / theory question 5 from the 2022 Neco Further Mathematics examination. This question covers Matrices, Determinants, Linear equations .
A 2 \times 2 matrix \(A\) is given by \(A = \begin{bmatrix} 2 & k \\ 3 & 5 \end{bmatrix}\) where \(k\) is an integer. The matrix is required to be invertible and its inverse must have only integer entries. Using this matrix, the system of linear equations \[\begin{cases} 2x + ky = 7 \\ 3x + 5y = 11 \end{cases}\] is to be solved. Answer the following: (a) Find the integer value of \(k\) that satisfies the above condition. (b) State the determinant of \(A\) and write down the inverse matrix \(A^{-1}\). (c) Using \(A^{-1}\), determine the ordered pair \((x, y)\) that satisfies the system.
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This is Neco 2022 Further Mathematics Question 5. It is one of the essay questions from the 2022 Neco Further Mathematics examination.
The question covers Matrices, Determinants, Linear equations .
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