Applications of matrices and determinants

Name: Applications of matrices and determinants
Uploaded: 2017-07-09T15:05:10+00:00
Duration: PTM15S3
Channel: Annabella Moore
Description: Applications of matrices and determinants

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) (b) 2 (c) (d) 4 The rank of the diagonal matrix is (a) (b) 2 (c) (d) 4

Choose the correct answer
3. If A = [ ], then the rank of AAT is (a) (b) 2 (c) (d) 0 , then the rank of AAT is (a) (b) 0 (c) (d) 2

5. If the rank of the matrix is 2, then  is a) (b) 2 (c) 3 (d) any real number 6. If A is a scalar matrix with scalar k  0, of order 3, then A–1 is (a) (b) (c) (d) KI

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 8. If A = is then (adj A)A = (a) (b) (c) (d)

9. If A is square matrix of order n then |adj A| is (a) |A|2 (b) |A|n (c) |A|n – (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)

11. The inverse of the matrix is (a) (b) (c) (d)

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 = (b) B is singular (c) B is non-singular (d) B = A

14. If A = then A12 = (a) (b) (c) (d) 15. The inverse of (a) (b) (c) (d)

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

17. The system of equations ax + y + z = 0; x + by + z = 0; x + y + cz = 0 has a non trivial solution then (a) (b) 2 (c) – (d) 0

18. If aex + bey = c; pex + qey = d and 1 = 2 = 3 = then the value of (x, y) is

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

20. Given (A, B) = (A) = number of unknowns, then the system has (a) unique solution (b) no solution (c) inconsistent (d) infinitely many solution

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

22. Given (A, B)  (A), then the system has (a) unique solution (b) no solution (c) 3 solutions (d) infinitely many solution

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

24. The value of (a) 0 (b) abc (c) a + b + c (d) – abc

25. The co-factor of – 1 in (a) (b) 48 (c) (d) – 38

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

The rank of the matrix is (a) 1 (b) (c) 0 (d) 8 The rank of the matrix is (a) 9 (b) (c) 1 (d) 5

If A and B are matrices conformable to multiplication then (AB)T is (a) ATBT (b) BTAT (c) AB (d) BA (AT)– 1 is equal to (a) A– (b) AT (c) A (d) (A– 1)T

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

Which of the following is not elementary transformation? (a) RiRj (b) Ri 2Ri + Rj (c) Ci Ci + Cj (d) Ri Ri + Cj Cramer’s rule is applicable only (with three unknowns) when (a)   0 (b)  = 0 (c)  = 0, x  0 (d)  = x = y = z = 0

Equivalent matrices are obtained by (a) taking inverses (b) taking transposes (c) taking adjoints (d) taking finite number of elementary transformations

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

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

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

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

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

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

Every homogeneous system (a) is always consistent
Every homogeneous system (a) is always consistent (b) has only trivial solution (c) has infinitely many solution (d) need not be consistent

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

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

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

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

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

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

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

THE END

Applications of matrices and determinants

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