ം /2014

1. The matrix equation >= 1,, where L, the identity matrix of order 2 and X is a square matrix
of order 2 over the field of real numbers has :
{A) No solutions (8) One solution
(C) Two solutions (D) Infinitely many solutions

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2. Let G ۳ | ab, ¢ யு and let + and . denote the matrix addition and multiplication
a

respectively. Then ‏سے‎

(ക (G, +)is a group but (G, .) is not a group

(B) (G..)is agroup but (G, +) is not a group.

(C) (G, .)is isomarphic with (C, .) where C is the group of complex numbers.
(D) None of the above

3, Let D be the group of symmetries of the square. Then
(ക) D has 4 subgroups of order 2 (9) D has 3 subgroups of arder 4

(ಲ) Order of D is 16 (D) Order of Dis 12
4. Which of the following sets is a subspace of the vector space R2?
(&) 1, ४) € ‏:قي‎ 22 +॥/2 = 1} ‏رم‎ 10, #) «782: = 1)
‏کا‎ 1೫ «82; ಇ] (೧) 10, «82: /-2]
5. G isa group of order 31. Then .
(^) Giscyclic (8) G is non-cyclic
(C) G is non-abelian (12) None of the above

6. LetT:R?— R?be the linear transformation defined by T(x, y, 2) ಹ (ಸ, ॥, 0). Then

1
(ക) (0,0, 4) is in the range space. (B) (೩ 5 ദും in the zero space.
(€) (1,1, 1) is in the range space. (D) (0, 0, 1) 15 in the zero space.

-10
7. The geometrical effect of the linear transformation associated with the matrix [ 0 ९८;

™
(ಗ) a rotation by an angle 5

(8) stretching along Y-axis and a reflection with respect lo Y-axis
(0 a stretching along X-axis
(D) a reflection with respect to X-axis

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