applications of matrices and determinants
DESCRIPTION
Applications of matrices and determinants. ONE MARK QUESTIONS. PREPARED BY: R.RAJENDRAN. M.A., M . Sc., M. Ed., K.C.SANKARALINGA NADAR HR. SEC. SCHOOL, CHENNAI-21. CHOOSE THE CORRECT ANSWER. The rank of the matrix is. (a) 1(b) 2 (c) 3 (d) 4. The rank of the diagonal matrix is. - PowerPoint PPT PresentationTRANSCRIPT
Applications of matrices and determinants
ONE MARK QUESTIONS
PREPARED BY:R.RAJENDRAN. M.A., M. SC., M. ED.,K.C.SANKARALINGA NADAR HR. SEC. SCHOOL,CHENNAI-21
CHOOSE THE CORRECT ANSWER
844
422
211
0
4
0
2
1
1. The rank of the matrix is
2. The rank of the diagonal matrix is
(a) 1 (b) 2
(c) 3 (d) 4
(a) 1 (b) 2
(c) 3 (d) 4
Choose the correct answer
3. If A = [2 0 1], then the rank of AAT is
(a) 1 (b) 2
(c) 3 (d) 0
3
2
1
A If 4. , then the rank of AAT is
(a) 3 (b) 0
(c) 1 (d) 2
Choose the correct answer
5. If the rank of the matrix is 2, then is
a) 1 (b) 2
(c) 3 (d) any real number
01
10
01
6. If A is a scalar matrix with scalar k 0, of order 3, then A–1 is
(a) (b)
(c) (d) KI
Ik
12
Ik
13
Ik
1
Choose the correct answer
7. If the matrix has an inverse then the value of k
is
a) K is any real number (b) k = – 4
(c) k – 4 (d) k 4
541
31
231
k
8. If A = is then (adj A)A =
(a) (b)
(c) (d)
1/50
01/5
10
01
5-0
05
43
12
50
05
Choose the correct answer
9. If A is square matrix of order n then |adj A| is
(a) |A|2 (b) |A|n
(c) |A|n – 1 (d) |A|
10. If A is matrix of order 3 then det (kA) is
(a) k3 det (A) (b) k2 det (A)
(c) k det (A) (d) det (A)
Choose the correct answer
11. The inverse of the matrix is
(a) (b)
(c) (d)
100
010
001
001
010
100
100
010
001
001
010
100
001
010
100
Choose the correct answer
12. If I is the matrix of order n, where k 0 is a constant,
then adj (k I) is
(a) kn (adj I) (b) k (adj I)
(c) k2 (adj I) (d) k n–1(adj I)
13. If A and B are any two matrices such that AB = 0 and A
is non-singular, then
(a) B = 0 (b) B is singular
(c) B is non-singular (d) B = A
Choose the correct answer
14. If A = then A12 =
(a) (b)
(c) (d)
600
00
1250
00
00
00
50
00
10
01
15. The inverse of
(a) (b)
(c) (d)
35-
1-2
3-1
52-
3-5-
1-3
25
13
2-1
53-
Choose the correct answer
16. In a system of 3 linear non-homogeneous equation with
three unknowns, if = 0 and x = 0, y 0 and z = 0 then
the system has
(a) unique solution (b) two solutions
(c) infinitely many solutions (d) no solutions
Choose the correct answer
17. The system of equations ax + y + z = 0; x + by + z = 0;
x + y + cz = 0 has a non trivial solution then
(a) 1 (b) 2
(c) – 1 (d) 0
cba 1
1
1
1
1
1
Choose the correct answer
18. If aex + bey = c; pex + qey = d and 1 =
2 = 3 = then the value of (x, y) is
qp
ba
qd
bc
dp
ca
1
3
1
2 , )(a
1
3
1
2 log,log )(b
2
1
3
1 log,log )(c
3
1
2
1 log,log )(b
Choose the correct answer
19. If the equations –2x + y + z = l; x – 2y + z = m;
x + y – 2z = n such that l + m + n = 0, then the system has
(a) a non-zero unique solution
(b) trivial solution
(c) infinitely many solution
(d) no solution
Choose the correct answer
20. Given (A, B) = (A) = number of unknowns, then the
system has
(a) unique solution
(b) no solution
(c) inconsistent
(d) infinitely many solution
Choose the correct answer
21. Given (A, B) = (A) < number of unknowns, then the
system has
(a) unique solution
(b) no solution
(c) 3 solutions
(d) infinitely many solution
Choose the correct answer
22. Given (A, B) (A), then the system has
(a) unique solution
(b) no solution
(c) 3 solutions
(d) infinitely many solution
Choose the correct answer
23. Which one of the following is not true regarding the
non-singular matrices A, B, C?
(a) A(adjA) = (adj A) A
(b) (AB)–1 = B–1 A–1
(c) (AB)T = BT AT
(d) (AT)–1 (A–1)T
Choose the correct answer
24. The value of
(a) 0 (b) abc
(c) a + b + c (d) – abc
c
b
a
00
00
00
Choose the correct answer
25. The co-factor of – 1 in
(a) 38 (b) 48
(c) 28 (d) – 38
242
531
753
Choose the correct answer
26. If the equation – 2x + y + z = l; x – 2y + z = m;
x + y – 2z = n such that l + m + n = 0, then the system
has
(a) a non-zero unique solution
(b) trivial solution
(c) infinitely many solution
(d) no solution
Choose the correct answer
27. The rank of the matrix is
(a) 1 (b) 2
(c) 0 (d) 8
28. The rank of the matrix is
(a) 9 (b) 2
(c) 1 (d) 5
21
42
12
17
Choose the correct answer
29. If A and B are matrices conformable to multiplication then (AB)T is
(a) ATBT (b) BTAT
(c) AB (d) BA
30. (AT)– 1 is equal to
(a) A– 1 (b) AT
(c) A (d) (A– 1)T
Choose the correct answer
31. If (A) = r then which of the following is correct?
(a) all the minors of order r which do not vanish
(b) A has atleast one minor of r which does not vanish
(c) A has atleast one (r + 1) order minor which vanishes
(d) all (r + 1) and higher order minors should not
vanish
Choose the correct answer
32. Which of the following is not elementary
transformation?
(a) RiRj (b) Ri 2Ri + Rj
(c) Ci Ci + Cj (d) Ri Ri + Cj
33. Cramer’s rule is applicable only (with three unknowns)
when
(a) 0 (b) = 0
(c) = 0, x 0 (d) = x = y = z = 0
Choose the correct answer
34. Equivalent matrices are obtained by
(a) taking inverses
(b) taking transposes
(c) taking adjoints
(d) taking finite number of elementary transformations
Choose the correct answer
35. In echelon form, which of the following is incorrect?
(a) Every row of A which has all its entries 0 occurs
below every row, which has a non-zero entry.
(b) The first non-zero entry in each non-zero row is 1
(c) The number of zeroes before the first non-zero
element in a row is less than the number of such
zeroes in the next row
(d) Two rows can have same number of zeroes before
the first non-zero entry
Choose the correct answer
36. If 0 then the system is
(a) consistent and has unique solution
(b) consistent and has infinitely many solution
(c) inconsistent
(d) Either consistent or inconsistent
Choose the correct answer
37. In the system of 3 linear equations with three
unknowns, if = 0 and one of x, y or z is non-zero
then the system is
(a) consistent (b) inconsistent
(c) consistent and the system reduces to two equations
(d) consistent and the system reduces to a single
equation
Choose the correct answer
38. In the system of 3 linear equations with three
unknowns, if = 0 and all 2 2 minors of = 0 and
atleast one 2 2 minor of x or y or z is non-zero then
the system is
(a) consistent
(b) inconsistent
(c) consistent and the system reduces to two equations
(d) consistent and the system reduces to a single
equation
Choose the correct answer
39. In the system of 3 linear equations with three
unknowns, if = 0, x = 0, y = 0, z = 0 and atleast one
2 2 minor of 0 then the system is
(a) consistent
(b) inconsistent
(c) consistent and the system reduces to two equations
(d) consistent and the system reduces to a single
equation
40. In the system of 3 linear equations with three unknowns,
if = 0 and all 2 2 minors of , x, y, z are zeros and
atleast one non-zero element is in then the system is
(a) consistent (b) inconsistent
(c) consistent and the system reduces to two equations
(d) consistent and the system reduces to a single
equation
41. Every homogeneous system
(a) is always consistent
(b) has only trivial solution
(c) has infinitely many solution
(d) need not be consistent
42. If (A) = (A,B) then the system is
(a) consistent and has infinitely many solution
(b) consistent
(c) consistent and has a unique solution
(d) inconsistent
43. If (A) = (A,B) = the number of unknowns then the
system is
(a) consistent and has infinitely many solution
(b) consistent
(c) consistent and has a unique solution
(d) inconsistent
Choose the correct answer
44. In the system of 3 linear equations with three
unknowns if (A) = (A,B) = 1 then the system is
(a) has a unique solution
(b) reduces to 2 equations and has infinitely many
solutions
(c) reduces to a single equation and has infinitely
many solution
(d) inconsistent
45. In the homogeneous system with three unknowns if
(A) = number of unknowns then the system has
(a) only trivial solution
(b) reduces to 2 equations and has infinitely many
solutions
(c) reduces to a single equation and has infinitely
many solution
(d) inconsistent
46. In the system of 3 linear equations with three unknowns,
in the non-homogeneous system if (A) = (A,B) = 2
then the system has
(a) has a unique solution
(b) reduces to 2 equations and has infinitely many
solutions
(c) reduces to a single equation and has infinitely many
solution
(d) inconsistent
Choose the correct answer
47. In the homogeneous system with three unknowns if
(A) < number of unknowns then the system has
(a) only trivial solution
(b) trivial solution and infinitely many non-trivial
solutions
(c) only non-trivial solutions
(d) no solution
Choose the correct answer
48. Which of the following statement is correct regarding
homogeneous system?
(a) always inconsistent
(b) has only trivial solution
(c) has only non trivial solutions
(d) has trivial solution only if rank of the coefficient
matrix is equal to the number of unknowns