Mathematical Methods of Physics-Eigenvalues and Eigenvectors (CSIR Physical Sciences): Questions 1 - 4 of 4

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Question number: 1

» Mathematical Methods of Physics » Eigenvalues and Eigenvectors

Appeared in Year: 2014

MCQ▾

Question

The column vector (aba) is a simultaneous eigenvector of A=(001010100) and B=(011101110) if,

(December)

Choices

Choice (4) Response

a.

b=aorb=2a

b.

b=0ora=0

c.

b=a2orb=a2

d.

b=2aorb=a

Question number: 2

» Mathematical Methods of Physics » Eigenvalues and Eigenvectors

Appeared in Year: 2012

MCQ▾

Question

The eigenvalue of the matrix A=(123246369) are, (June)

Choices

Choice (4) Response

a.

(0, 1,13)

b.

(0, 7,7)

c.

(0, 0,14)

d.

(1, 4,9)

Question number: 3

» Mathematical Methods of Physics » Eigenvalues and Eigenvectors

Appeared in Year: 2011

MCQ▾

Question

A 3×3 matrix M has Tr[M]=6,Tr[M2]=26,Tr[M3]=90 . Which of the following can be a possible set of eigenvalue of M? -

(December)

Choices

Choice (4) Response

a.

{1,1, 4}

b.

{1, 0,7}

c.

{1, 3,4}

d.

{2,2,2}

Passage

In the absence of an applied torque a rigid body with three distances principal moments of inertia given by I1,I2andI3 is rotating freely about a fixed point inside the body. The Euler equations for the components of its angular velocity (ω1,ω2,ω3) are

ω˙1=I2I1I1ω2ω3,ω˙2=(I3I1)I2ω1ω3,ω˙3=I1I2I3ω1ω2 (June)

Question number: 4 (1 of 1 Based on Passage) Show Passage

» Mathematical Methods of Physics » Eigenvalues and Eigenvectors

Appeared in Year: 2011

MCQ▾

Question

The equilibrium points in (ω1,ω2,ω3) space are –

Choices

Choice (4) Response

a.

(1,1, 0),(1, 0,1)and(0,1, 1)

b.

(1, 1,0),(1, 0,1)and(0, 1,1)

c.

(1, 0,0),(0, 1,0)and(0, 0,1)

d.

(1, 1,1),(1,1,1)and(0, 0,0)

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