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

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

Matrices

Exercise 3.1

1. In the matrix \(A=\begin{bmatrix}2 & 5 & 19 & -7 \\ 35 & -2 &  5\over 2 & 12 \\ \sqrt{3} & 1 & -5 & 17 \end{bmatrix}\), write :

(i) The order of the matrix

(ii) The number of elements

(iii) Write the elements \(a_{13}, a_{21}, a_{33}, a_{24}, a_{23}\).

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

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

4. Construct a 2 × 2 matrix, \(A=[a_{ij}]\), whose elements are given by :

(i) \(a_{ij}={{(i+j)^2} \over 2}\)

(ii) \(a_{ij}={i \over j}\)

(iii) \(a_{ij}={{(i+2j)^2} \over 2}\).

5. Construct a 3 × 4 matrix, whose elements are given by :

(i) \(a_{ij}={1 \over 2}|-3i+j|\)

(ii) \(a_{ij}={2i-j}\)

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) \(\begin{bmatrix}x+y+z \\ x+z \\ y+z\end{bmatrix}\)=\(\begin{bmatrix}9\\ 5 \\7 \end{bmatrix}\)

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) \(x={-1\over 3}, y=7\)
(B) Not possible to find
(C) \(y=7, x={-2\over 3}\)
(D) \(x={-1\over 3}, y={-2\over 3}\)

10. 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