Page 1 - Work sheet

XII-CH3-MATRIX

WORK SHEET

Answer all the questions:

1. Total number of possible matrices of order 3x3 with each entry 2 or 0 is
(a ) 9 ( b ) 27 ( c ) 81 ( d ) 512
−1
−1 − −1 −1
1 1
2. If A= , B= , then A – B is equal
−1
−1 −1 −1 −

to :
(a ) I ( b ) 0 ( c ) 2I ( d ) ½ I

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3. If A and B are square matrices of same order , then AB – BA is a
( a ) skew symmetric ( b ) null matrix ( c ) symmetric ( d ) none of these

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4. If A is a matrix of order m x n and B is a matrix such that AB and BA are both
defined then order of the matrix B is:
(a ) m x m ( b ) n x n ( c ) n x m ( d ) m x n

3
5. If A is a symmetric matrix , then A is a ………….. matrix.
6. Write the number of all possible matrices of order 2x2 with each entry 1,2 or 0 .

 3  4
7. If A    , find a matrix B such that AB = I.
  1 2 
8. Express the matrix A as the sum of symmetric and skew symmetric matrix,
2 4 −6
where A = 7 3 5
1 −2 4
 cosx  sinx 0

9. If f(x)    sinx cosx 0 , show that f(x) f(y) f(x y) 

  0 0 1 

2 −1 −1 −8 −10
10. Find the matrix X so that: 0 1 X = 3 4 0
−2 4 10 20 10
3 0 −1
11. Find the inverse of the following matrix by elementary row operations: 2 3 0
0 4 1

cos   isin   cosn   isinn  

12. If A    , then prove by induction that A  n   ,n N
 isin  cos   isinn  cosn  