Neco 2017 Further Mathematics Question 29

Practice objective / multiple choice question 29 from the 2017 Neco Further Mathematics examination.

Neco 2017 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 29 NECO • 2017 • FURTHER_MATHEMATICS • objective

Let \(T:\mathbb{R}^{2}\to\mathbb{R}^{2}\) be represented by \(A=\begin{pmatrix}0&-1\\1&0\end{pmatrix}\) (a rotation of \(90^{\circ}\) anticlockwise) and \(S:\mathbb{R}^{2}\to\mathbb{R}^{2}\) by \(B=\begin{pmatrix}2&1\\0&3\end{pmatrix}.\) Define the composite transformation \(C=S\circ T\).\n(a) Find the matrix of \(C\).\n(b) Determine the eigenvalues of \(C\).\n(c) Compute \(C^{3}\mathbf{v}\) for \(\mathbf{v}=\begin{pmatrix}1\\0\end{pmatrix}.\)

Answer Options

A. C=\\begin{pmatrix}0&-2\\\\3&1\\end{pmatrix}; eigenvalues = (1\\pm i\\sqrt{23})\\/2; C^{3}\\mathbf{v}=(-11,-15)
B. C=\\begin{pmatrix}1&-2\\\\3&0\\end{pmatrix}; eigenvalues = (1\\pm i\\sqrt{23})\\/2; C^{3}\\mathbf{v}=(-10,-14)
Correct Answer C. C=\begin{pmatrix}1&-2\\3&0\end{pmatrix}; eigenvalues = (1\pm i\sqrt{23})/2; C^{3}\mathbf{v}=(-11,-15)
D. C=\\begin{pmatrix}1&-2\\\\3&0\\end{pmatrix}; eigenvalues = (2\\pm i\\sqrt{23})\\/2; C^{3}\\mathbf{v}=(-11,-15)
Correct Answer
C
Correct Option:
C=\begin{pmatrix}1&-2\\3&0\end{pmatrix}; eigenvalues = (1\pm i\sqrt{23})/2; C^{3}\mathbf{v}=(-11,-15)

About This Question

This is Neco 2017 Further Mathematics Question 29. It is one of the objective questions from the 2017 Neco Further Mathematics examination.

Difficulty level: Hard .

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