MATRICES and DETERMINANTS

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SOME IMPORTANT QUESTIONS :-

1. If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a (A) Skew symmetric matrix

(B) Null matrix

(C) Symmetric matrix

(D) None of these Solution

Solution: (A) is correct answer since

(AB′ –BA′)′ = (AB′)′ – (BA′)′

= (BA′ – AB′) = – (AB′ –BA′)

2. If A and B are two skew symmetric matrices of same order, then AB is symmetric matrix if ________.

Solution: AB = BA

3. If A and B are matrices of same order, then (3A –2B)′ is equal to ________.

Solution: 3A′ –2B′.

4. Addition of matrices is defined if order of the matrices is ________ Solution: Same.

5. If two matrices A and B are of the same order, then 2A + B = B + 2A. Solution: True

6. Matrix subtraction is associative

Solution: False

7. For the non singular matrix A, (A′) –1 = (A–1)′.

Solution: True

8. AB = AC ⇒ B = C for any three matrices of same order.

Solution: False

9.If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?

10. Give an example of matrices A, B and C such that AB = AC, where A is nonzero matrix, but B ≠ C.

11. Show that A′A and AA′ are both symmetric matrices for any matrix A.

12. If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A′BA is skew symmetric.

13. If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405. 52.

14. If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.

15. If A is a matrix of order 3 × 3, then number of minors in determinant of A are ________.

16. The sum of the products of elements of any row with the co-factors of corresponding elements is equal to _________.

17. If A is a matrix of order 3 × 3, then |3A| = _______ .

18. Show that the points (a + 5, a – 4), (a – 2, a + 3) and (a, a) do not lie on a straight line for any value of a.

FOR MORE QUESTIONS PLESE CHECK :

https://help4nda.blogspot.com/2022/01/most-important-questions-of-matrices.html

NDA MATHEMATICS NOTES :

#COMPLEX NO.

#SET THEORY

#RELATION

#PERMUTATION AND COMBINATION

#PROBABILITY

QUESTIONS OF PROBABILITY

#VECTOR

#LOGARITHM

#BINARY NO.

#TRIGONOMETRY

#INVERSE TRIGONOMETRY FUNCTION

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MATRICES and DETERMINANTS

SOME IMPORTANT QUESTIONS :-

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