2. If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?
Matrices
Exercise 3.1
(iii) Write the elements (a_{13}, a_{21}, a_{33}, a_{24}, a_{23}).
4. Construct a 2 × 2 matrix, (A=[a_{ij}]), whose elements are given by :
(i) (a_{ij}={{(i+j)^2} over 2})
(iii) (a_{ij}={{(i+2j)^2} over 2}).
5. Construct a 3 × 4 matrix, whose elements are given by :
(i) (a_{ij}={1 over 2}|-3i+j|)
6. Find the values of x, y and z from the following equations :
(i) (begin{bmatrix}4 & 3 \ x & 5 end{bmatrix})=(begin{bmatrix}y & z \ 1 & 5 end{bmatrix})
(ii) (begin{bmatrix}x+y & 2 \ 5+z & xy end{bmatrix})=(begin{bmatrix}6 & 2 \ 5 & 8 end{bmatrix})
(iii) (begin{bmatrix}x+y+z \ x+z \ y+zend{bmatrix})=(begin{bmatrix}9\ 5 \7 end{bmatrix})
7. Find the value of a, b, c and d from the equation :
(begin{bmatrix}a-b & 2a+c \ 2a-b & 3c+d end{bmatrix})=(begin{bmatrix}-1 & 5 \ 0 & 13 end{bmatrix})
8. (A = {[a_{ij}]}_{m×n}) is a square matrix, if
(A) m < n
(B) m > n
(C) m = n
(D) None of these
9. Which of the given values of x and y make the following pair of matrices equal
(begin{bmatrix}3x+7 & 5 \ y+1 & 2-3x end{bmatrix}), (begin{bmatrix}0 & y-2 \ 8 & 4 end{bmatrix})
(A) (x={-1over 3}, y=7)
(B) Not possible to find
(C) (y=7, x={-2over 3})
(D) (x={-1over 3}, y={-2over 3})
10. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is :
