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## Chapter: 12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants

Business Maths and Statistics : Applications of Matrices and Determinants: Multiple choice questions with Answers, Solution and Explanation - Book back 1 mark questions and answers with solution for Exercise Problems

1. If A=(1 2 3), then the rank of AAT is

(a) 0

(b) 2

(c) 3

(d) 1 2. The rank of m ├Ś n matrix whose elements are unity is

(a) 0

(b) 1

(c) m

(d) n 3. If is a transition probability matrix, then at equilibrium A is equal to

(a) 1/4

(b) 1/5

(c) 1/6

(d) 1/8 4. If A = , then Žü(A) is

(a) 0

(b) 1

(c) 2

(d) n 5. The rank of the matrix is

(a) 0

(b) 1

(c) 2

(d) 3 6. The rank of the unit matrix of order n is

(a) n ŌłÆ1

(b) n

(c) n + 1

(d) n2 7. If Žü (A) = r then which of the following is correct?

(a) all the minors of order r which does not vanish

(b) A has at least one minor of order r which does not vanish

(c) A has at least one (r+1) order minor which vanishes

(d) all (r+1) and higher order minors should not vanish

8. If A = then the rank of AAT is

(a) 0

(b) 1

(c) 2

(d) 3 9. If the rank of the matrix is 2. Then ╬╗ is

(a) 1

(b) 2

(c) 3

(d) only real number 10. The rank of the diagonal matrix (a) 0

(b) 2

(c) 3

(d) 5 11. If T = is a transition probability matrix, then the value of x is

(a) 0.2

(b) 0.3

(c) 0.4

(d) 0.7 12. Which of the following is not an elementary transformation?

(a) Ri Ōåö Rj

(b) Ri ŌåÆ 2 Ri + 2Cj

(c) Ri ŌåÆ 2 Ri ŌłÆ 4Rj

(d) Ci ŌåÆ Ci + 5Cj 13. If Žü(A) = Žü(A, B) then the system is

(a) Consistent and has infinitely many solutions

(b) Consistent and has a unique solution

(c) Consistent

(d) inconsistent 14. If Žü(A) = Žü(A, B) the number of unknowns, then the system is

(a) Consistent and has infinitely many solutions

(b) Consistent and has a unique solution

(c) inconsistent

(d) consistent 15. If Žü ( A) ŌēĀ Žü ( A, B) , then the system is

(a) Consistent and has infinitely many solutions

(b) Consistent and has a unique solution

(c) inconsistent

(d) consistent 16. In a transition probability matrix, all the entries are greater than or equal to

(a) 2

(b) 1

(c) 0

(d) 3 17. If the number of variables in a non- homogeneous system AX = B is n, then the system possesses a unique solution only when

(a) Žü ( A ) = Žü ( A, B ) > n

(b) Žü ( A ) = Žü ( A, B ) = n

(c) Žü ( A ) = Žü ( A, B ) < n

(d) none of these

18. The system of equations 4x + 6 y = 5, 6x + 9 y = 7 has

(a) a unique solution

(b) no solution

(c) infinitely many solutions

(d) none of these 19. For the system of equations x + 2 y + 3z = 1, 2x + y + 3z = 2 5x + 5y + 9z = 4

(a) there is only one solution

(b) there exists infinitely many solutions

(c) there is no solution

(d) None of these 20. If |A| ŌēĀ 0, then A is

(a) non- singular matrix

(b) singular matrix

(c) zero matrix

(d) none of these

21. The system of linear equations x + y + z = 2, 2x + y ŌłÆ z = 3, 3x + 2 y + k = 4 has unique solution, if k is not equal to

(a) 4

(b) 0

(c) ŌĆō4

(d) 1 22. CramerŌĆÖs rule is applicable only to get an unique solution when

(a) ╬öz ŌēĀ 0

(b) ╬öx ŌēĀ 0

(c) ╬ö ŌēĀ 0

(d) ╬öy ŌēĀ 0

23. If then (x y) is Ans: (d) 24. |An ├Śn| = 3 |adjA| = 243 then the value n is

(a) 4

(b) 5

(c) 6

(d) 7 25. Rank of a null matrix is

(a) 0

(b) ŌĆō1

(c) Ōł×

(d) 1 Tags : Applications of Matrices and Determinants , 12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants
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12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants : Choose the correct answer | Applications of Matrices and Determinants