Neco 2021 Further Mathematics Question 41

Practice objective / multiple choice question 41 from the 2021 Neco Further Mathematics examination.

Neco 2021 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 41 NECO • 2021 • FURTHER_MATHEMATICS • objective

Let \(A=\begin{pmatrix}a&b\\c&d\end{pmatrix}\) be the matrix of a linear transformation on \(\mathbb{R}^2\). It is known that \(A\begin{pmatrix}1\\2\end{pmatrix}=\begin{pmatrix}3\\5\end{pmatrix}\) and \(A\begin{pmatrix}2\\-1\end{pmatrix}=\begin{pmatrix}k\\4\end{pmatrix}\). Moreover, the transformation doubles the area of every parallelogram, i.e. \(|\det A|=2\). Find the value of \(k\) and determine the matrix \(A\).

Answer Options

Correct Answer A. k = \frac{22}{5}; \; A = \begin{pmatrix}\frac{59}{25}&\frac{8}{25}\\\frac{65}{25}&\frac{6}{5}\end{pmatrix}
B. k = \\frac{22}{5}; \\; A = \\begin{pmatrix}\\frac{59}{25}&\\frac{9}{25}\\\\\\\\\\\ rac{65}{25}&\\frac{6}{5}\\end{pmatrix}
C. k = \\frac{24}{5}; \\; A = \\begin{pmatrix}\\frac{59}{25}&\\frac{8}{25}\\\\\\\\\\\ rac{65}{25}&\\frac{6}{5}\\end{pmatrix}
D. k = \\frac{22}{5}; \\; A = \\begin{pmatrix}\\frac{60}{25}&\\frac{8}{25}\\\\\\\\\\\ rac{65}{25}&\\frac{6}{5}\\end{pmatrix}
Correct Answer
A
Correct Option:
k = \frac{22}{5}; \; A = \begin{pmatrix}\frac{59}{25}&\frac{8}{25}\\\frac{65}{25}&\frac{6}{5}\end{pmatrix}

About This Question

This is Neco 2021 Further Mathematics Question 41. It is one of the objective questions from the 2021 Neco Further Mathematics examination.

Difficulty level: Hard .

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