Matrices - avaquant611934072.files.wordpress.com · Matrices 2 6. If 0 2 1 25 34 1 3 4 43 01 x y ª...
Transcript of Matrices - avaquant611934072.files.wordpress.com · Matrices 2 6. If 0 2 1 25 34 1 3 4 43 01 x y ª...
Matrices
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SET-A
1. If A=1 -2
3 0
, B=1 4
,2 0
0 1C=
-1 0
then 5A-3B+2C is equal to
5A-3B+2C is equal to
a.8 7
-20 -9
b. 8 -20
7 -9
c.8 20
7 9
d. 8 20
7 9
2. If A=1 1 1
,3 3 3
-2 3
B= 1 -5 ,
4 1
then AB is equal to
a. -3 -1
9 -3
b. 3 -1
9 -3
c. -3 1
9 3
d. 3 1
-9 3
3. If A=1 2 1 0
,B=3 0 2 3
then which of the following is correct?
a. 2A A b.
2B B
c. AB=BA d. None of these
4. If A=
1 2 3
2 1 2 , then A is
3 2 1
a. A symmetric matrix b. A skew
c.A singular matrix d. Non singular matrix
5. If A=0 1
0 0
and I is the unit matrix of order 2, then 2
a I+bA , where ‘a’ and ‘b’ are
given constants, is equal to
a. 2 2a b A b.
2 2a abA
c. 2a abA d.
2 2a b A
Matrices
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6. If 0 2 1 2 5 3 4
,1 3 4 4 3 01
x
y
then ordered pair (x,y) is
a. 1, 2 b. 1,2
c. 1,2 d. 1, 2
7. If A= cos sin 1 0
and A adj A-sin cos 0 1
then is equal to
a.1 b. 2
c. 3 d.1/2
8. If A=1 12
1 1
and A , thena ba b
b a b a
a. 2 2 2 2
1 1,a a b b a b b.
2 2
1 12 ,a ab b a b
c. 2 2
1 1,a a b b ab d.
2 2
1 1, 2a a b b ab
9. If 1 2 5
,2 1 4
x
y
then the value of
2 2x y
xy
is equal to
a.5
2 b.
3
2
c.13
6 d.
13
6
10. If A=2 1
1 2
and A2-4A-nl=0, where I is the unit matrix of order 2, then
a.1
3n b.
1
3n
c. 3n d. 3n
11. If for the matrices A and B, AB=4 and BA=B, then A2 is equal to
a. I b. A
c. B d. None of these
12. The matrix
1 2
1 2 5
2 1 1
a
will be non-singular if
Matrices
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a.a=1 b. 1a
c. 9a d. 9a
13. If
1 0 1 1
1 1 0 1 ,
0 1 1 2
x
y
z
then ordered triplet (y, x, z) is
a. 0, 1, 2 b. 1, 0, 2
c. 1, 2,0 d. 0,2, 1
14. If A 1 2 4 1
,3 1 7 7
then A equals to
a.1 1
2 3
b.1 1
2 3
c.1 1
2 3
d. 1 1
2 3
15. If T
cos sinA= , then A.A
-sin cos
is equal to
a. 0 0
0 0
b. 1 1
1 1
c. 1 0
0 1
d. 0 1
1 0
16. If A=n
1 1, then A , , is equal to
0 1n N
a.n n
0 n
b. 1 n
0 1
c.n 1
0 1
d. 1 1
0 n
17. If ‘A’ is a matrix of order m x n, and Im, In represent the unit matrices of order ‘m’ and
‘n’ respectively, then
a.m n
I A=A=AI b. m n
AI A=I A
c.m n
AI =A=AI A d. m n
I A=A=I A
Matrices
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18. Every square matrix can be expressed as the sum of
a. Two symmetric
b. Two skew symmetric matrices
c. a symmetric and a skew symmetric matrix
d. A singular matrix and nonsingular matrix
19. If A is symmetric matrix and B is a skew symmetric matrix, then for any nN, which of
the followings is not correct?
a. An b. An is symmetric if n is odd
c. Bn is skew symmetric if n is odd d. Bn is symmetric if n is even
20. If a2+b2+c2+d2=1, and -1
a+ib c+idA= , then A
c+id a-ib
is equal to
a.a+ib id c
c id a ib
b.a-ib id c
c id a ib
c. a-ib id c
c id a ib
d. a+ib id c
c id a ib
Matrices
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SET-B
1. Which of the following statements is correct?
a. A skew-symmetric matrix of odd order is always invertible
b. Askew-symmetric matrix of odd order is always non-invertible
c. A skew-symmetric matrix of even order is always non-invertible
d. None of these
2. If A=
2
n
2
0 0 and A ,
0 0
ab b
a ab
then minimum value of ‘n’ is equal to
a. 2 b. 4
c.6 d. 3
3. If A and B are square matrices such that AB=B and BA=A, then A2+B2 is always equal
to
a. 2AB
b. 2BA
c. A+B
d. AB
4. If A=3 4
n n
, then An is equal to (nN)
a.3 4n n
n n
b.
3 4
1 1
nn
n
c. 2 5n n
n n
d. None of these
5. If A+B=1 0
1 1
and A-2B=1 1
,0 1
then A is equal to
a. 1 1
2 1
b.
2 1
3 3
1 2
3 3
c.
1 1
3 3
2 1
3 3
d. 2
13
11
3
Matrices
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6. If a is skew-symmetric matrix of order ‘n’ then the maximum number of non-zero
elements in ‘a’ is
a. 1
2
n n b.
2 1 1
6
n n n
c. 1n n d.
21
2
n n
7. If ‘A’ is a symmetric matrix of order ‘n’ , then maximum number of non-zero elements
in ‘A’ is
a. n2 b. n (n-1)
c. 1
2
n n d.
1
2
n n
8. The minimum number of zero elements in an upper triangular matrix of order nn is
a. 1
2
n n
b. 1
2
n n
c. 2 1
2
n
d. 2 1
2
n
9. If A=1 2 1 4 4 8
,B= and A.B.C=3 0 2 3 3 7
then C equals to
a.
59
3111 1
22 6
b.
59
3111 1
22 6
c.
59
3111 1
22 6
d. None of these
10. If -1
1 2 3
A= 0 1 2 , then A
0 0 1
is equal to
Matrices
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a.
1 2 1
0 1 2
0 0 1
b.
1 0 0
2 1 0
1 -2 1
c.
1 2 1
0 1 2
0 0 1
d. None of these
11. If A-B=1 2
2 4
and A+B=3 2
,2 0
Then AB equals to
a.2 4
-4 -4
b. 2 4
-4 -4
c.2 -4
4 4
d. 2 -4
4 -4
12. If A=
1 2 21
2 1 23
2x y
is a orthogonal matrix, then the value of x +y is equal to
a. 3 b.-3
c.0 d. 1
13. The total number of matrices that can be formed using 5 different letters such that no
letter is repeated in any matrix, is equal to
a. (5!) b. 2 (5!)
c. 2. 56 d. 56
14. 2 2ijA= aij and a ,
n ni j
then ‘A’ is necessarily
a. A unit matrix b. A zero matrix
c. A symmetric matrix d. A skew symmetric matrix
15. If 1 1 2 2
1 1 1 2
2 2
cos sin 0 cos 0 sinx
A x sinx cos 0 andA x = 0 1 0
sin 0 cos0 0 1
x x x
x
x x
then 1
1 2A x .A x
is equal
to
a. 1 2A x .A x b. 1 2
A -x .A -x
c. 2 1A x .A x d. 2 1
A -x .A x
Matrices
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16. If A=2
1 1 1
21 1 1
cos sin cos,
sin cos sin
x x x
x x x
then 1 2x x is equal to
a.0 b. , 1n n
c. 2 1 , 12
n n
d. 2 , 1n n
17. If A=
1 tan 1 tan2 2
,B=x
tan 1 tan 12 2
x x
x
then A. B-1 is equal to
a. cos sin
sin cos
x x
x x
b.cos sin
sin cos
x x
x x
c. cos sin
sin cos
x x
x x
d. cos sin
sin cos
x x
x x
18. If A= -1
2 2
,, then A
,
i j i jaij whereaij
i j i j
is equal to
a.
10
3
10
3
b.
2 1
9 3
10
3
c.
10
3
1 2
3 9
d. None of these
19. If 1 2
1,0 0 1 cos sinI ,I and A=
0,1 1 0 -sin cos
and ‘A’ can be written as
a. 1 2
I cos I sin b. 1 2I cos I sin
c. 1 2
I sin I cos d. 1 2
I cos I sin
20. If
1 2 1 0
0 1 0 2 ,
3 1 1 1
x
y
z
then ordered triplet (x,y,z) is
a. 9 7
,2,4 4
b. 7 9
,2,4 4
c. 9 7
, 2,4 4
d.
7 9, 2,
4 4
Matrices
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Answers Exercise-1 Matrices
1. b 2. b 3. d 4. a 5. d 6. a 7. a 8. d 9. a 10. c
11. b 12. b 13. b 14.a 15. c 16.b 17. a 18. c 19. b 20. c
Answers Exercise-2 Matrices
1. d 2. a 3. c 4. d 5. c 6. c 7. a 8. a 9. b 10. c
11. a 12. b 13. b 14.d 15. d 16.c 17. c 18. a 19. a 20. b
Matrices
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Matrices
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Matrices
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Matrices
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Answers Exercise-1 Quadratic Equation and Expressions
1. a 2. a 3. b 4. a 5. b 6. d 7. d 8. b 9. a 10. b
11. b 12. c 13. b 14.d 15. d 16.b 17. d 18. b 19. d 20. a
21. c 22. a 23. c 24. b 25. c
Answers Exercise-2 Quadratic Equation and Expressions
1. d 2. a 3. d 4. b 5. c 6. b 7. a 8. a 9. b 10. b
11. d 12. c 13. c 14.b 15. c 16.b 17. b 18. d 19. b 20. a
21. a 22. a 23. d 24. c 25. c
Answers Exercise-3 Quadratic Equation and Expressions
Matrices
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1. d 2. b 3. a 4. b 5. c 6. a 7. c 8. d 9. a 10. b
11. c 12. a 13. a 14.a 15. c 16. a 17. b 18. c 19. a 20. d
21. d 22. a 23. b 24. b 25. a