Exercise 3.1

5A 35 2 12 2 / 173 1 5 /  −    = −    −  , write: (i) The order of the matrix, (ii) The number of elements, (iii) Write the elements a13, a21, a33, a24, a23.

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

Construct a 2 × 2 matrix, A = [aij], whose elements are given by: (i) 2( ) / ij i ja += (ii) ij ia j = (iii) 2( 2 ) ij i ja +=

Construct a 3 × 4 matrix, whose elements are given by: (i) 1 | 3 |2 ija i j= − + (ii) 2ija i j= −

Find the values of x, y and z from the following equations: (i) 4 3 / 5 1 5 / y z / x     =       (ii) 2 6 2 / 5 5 8 / x y z xy +    =   +    (iii) 9 5/7

x z / y z + +       + =       +   

Find the value of a, b, c and d from the equation: 2 1 5 2 3 0 13

− + −   =   − +   

A = [aij]m × n\ is a square matrix, if (A) m < n (B) m > n (C) m = n (D) None of these

1 2 3 / x / y x +   + −  , 0 2 8 4 y −     (A) 1, 73x y −= = (B) Not possible to find (C) y = 7, 2 3x −= (D) 1 2,3 3x y − −= =

The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is: (A) 27 (B) 18 (C) 81 (D) 512