Gce Model Questions Vol1 2020 Further Mathematics Question 35

Practice objective / multiple choice question 35 from the 2020 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2020 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 35 GCE_MODEL_QUESTIONS_VOL1 • 2020 • FURTHER_MATHEMATICS • objective

A linear transformation \(T:\mathbb{R}^{2}\to\mathbb{R}^{2}\) maps the points \(A(1,2)\), \(B(3,5)\) and \(C(4,1)\) to \(A'(4,5)\), \(B'(11,12)\) and \(C'(9,-1)\) respectively.\n\n(a) Find the matrix of \(T\).\n(b) Compute the determinant of this matrix and state the factor by which areas are scaled under \(T\).\n(c) Find the inverse matrix \(T^{-1}\).\n(d) Using \(T^{-1}\), determine the original point \(P\) that is mapped to \(P'(7,2)\).

Answer Options

A. Matrix \(\begin{pmatrix}3&0\\-1&2\end{pmatrix}\); determinant 6 (area scaling factor 6); inverse \(\frac{1}{6}\begin{pmatrix}2&0\\1&3\end{pmatrix}\); original point \((13\/6,\;7\/6)\).
Correct Answer B. Matrix \(\begin{pmatrix}2&1\\-1&3\end{pmatrix}\); determinant 7 (area scaling factor 7); inverse \(\frac{1}{7}\begin{pmatrix}3&-1\\1&2\end{pmatrix}\); original point \((19/7,\;11/7)\).
C. Matrix \(\begin{pmatrix}2&-1\\1&3\end{pmatrix}\); determinant 5 (area scaling factor 5); inverse \(\frac{1}{5}\begin{pmatrix}3&1\\-1&2\end{pmatrix}\); original point \((17\/5,\;9\/5)\).
D. Matrix \(\begin{pmatrix}1&2\\-2&4\end{pmatrix}\); determinant 8 (area scaling factor 8); inverse \(\frac{1}{8}\begin{pmatrix}4&-2\\2&1\end{pmatrix}\); original point \((15\/8,\;13\/8)\).
Correct Answer
B
Correct Option:
Matrix \(\begin{pmatrix}2&1\\-1&3\end{pmatrix}\); determinant 7 (area scaling factor 7); inverse \(\frac{1}{7}\begin{pmatrix}3&-1\\1&2\end{pmatrix}\); original point \((19/7,\;11/7)\).

About This Question

This is Gce Model Questions Vol1 2020 Further Mathematics Question 35. It is one of the objective questions from the 2020 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Hard .

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