Neco 2021 Further Mathematics Question 39

Practice objective / multiple choice question 39 from the 2021 Neco Further Mathematics examination.

Neco 2021 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 39 NECO • 2021 • FURTHER_MATHEMATICS • objective

In the plane, let \(T\) be the transformation that first rotates a vector anticlockwise through \(45^{\circ}\) and then reflects it in the line \(y=x\).\\n(a) Find the standard matrix \(A\) of \(T\).\\n(b) Determine the image of the vector \(v=(3,-1)\) under \(T\).\\n(c) Find the eigenvalues of \(A\).

Answer Options

A. A = (√2\/2)[[1,-1],[-1,-1]]; T(3,-1) = (-√2, 0); eigenvalues = 2, -2
Correct Answer B. A = (√2/2)[[1,1],[1,-1]]; T(3,-1) = (√2, 2√2); eigenvalues = 1, -1
C. A = (√2\/2)[[2,0],[0,-2]]; T(3,-1) = (2√2, -2√2); eigenvalues = √2, -√2
D. A = (√2\/2)[[0,1],[1,0]]; T(3,-1) = (0, √2); eigenvalues = 0, 1
Correct Answer
B
Correct Option:
A = (√2/2)[[1,1],[1,-1]]; T(3,-1) = (√2, 2√2); eigenvalues = 1, -1

About This Question

This is Neco 2021 Further Mathematics Question 39. It is one of the objective questions from the 2021 Neco Further Mathematics examination.

Difficulty level: Hard .

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