Gce Model Questions Vol1 2023 Further Mathematics Question 12

Practice objective / multiple choice question 12 from the 2023 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2023 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 12 GCE_MODEL_QUESTIONS_VOL1 • 2023 • FURTHER_MATHEMATICS • objective

A linear transformation \(T:\mathbb{R}^2\to\mathbb{R}^2\) is represented by a matrix \(A=\begin{pmatrix}a&b\\c&d\end{pmatrix}\). It is known that \(T\bigl(1,2\bigr)=(3,5)\) and \(T\bigl(2,-1\bigr)=(k,4)\). Moreover, the transformation scales areas by a factor of \(3\). Find the value of \(k\) and give the matrix \(A\).

Answer Options

Correct Answer A. k = 27/5; A = [[69/25, 3/25], [13/5, 6/5]]
B. k = 23/5; A = [[65/25, 4/25], [12/5, 7/5]]
C. k = 31/5; A = [[71/25, 2/25], [14/5, 5/5]]
D. k = 27/4; A = [[68/25, 3/20], [13/5, 6/5]]
Correct Answer
A
Correct Option:
k = 27/5; A = [[69/25, 3/25], [13/5, 6/5]]

About This Question

This is Gce Model Questions Vol1 2023 Further Mathematics Question 12. It is one of the objective questions from the 2023 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Hard .

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