How many entries are there in a p × q matrix.

Let us consider a set of numbers a i j ( i = 1 , 2 , … m ; j = 1 , 2 , 3 … . n ) . We can arrange them in a rectangular array as follows: A = a 11 a 12 … a 1 n a 21 a 22 … a 2 n a 31 a 32 … a 3 n ⋮ ⋮ ⋮ ⋮ a m 1 a m 2 … a m n Here, A = a i j m × n is called a matrix of order m × n . Each a i j entry is called the element of the matrix and it is the j t h element of the i t h row. Also, it can be observed that there are m n entries in a matrix of order m × n . Here m = p and n = q Hence, there are p q entries in a matrix of order p × q .

How many entries are there in a p × q matrix.

Let us consider a set of numbers a i j ( i = 1 , 2 , … m ; j = 1 , 2 , 3 … . n ) . We can arrange them in a rectangular array as follows: A = a 11 a 12 … a 1 n a 21 a 22 … a 2 n a 31 a 32 … a 3 n ⋮ ⋮ ⋮ ⋮ a m 1 a m 2 … a m n Here, A = a i j m × n is called a matrix of order m × n . Each a i j entry is called the element of the matrix and it is the j t h element of the i t h row. Also, it can be observed that there are m n entries in a matrix of order m × n . Here m = p and n = q Hence, there are p q entries in a matrix of order p × q .

Give an example of 3 × 1 matrix.

A matrix is a rectangular array of numbers (any system of numbers), arranged in rows and columns. If there are m rows, and n columns in a matrix, it is called a matrix of order m × n , and it is given as follows: A = a 11 a 12 … a 1 n a 21 a 22 … a 2 n a 31 a 32 … a 3 n ⋮ ⋮ ⋮ ⋮ a m 1 a m 2 … a m n m × n Each a i j ( i = 1 , 2 , … m ; j = 1 , 2 , 3 … n ) entry is called the element of the matrix and it is the j t h element of the i t h row Now, matrix of order 3 × 1 is a matrix of 3 rows and 1 column. For example: 1 2 3 3 × 1 .

Give an example of 2 × 2 matrix.

A matrix is a rectangular array of numbers (any system of numbers), arranged in rows and columns. If there are m rows, and n columns in a matrix, it is called a matrix of order m × n , and it is given as follows: A = a 11 a 12 … a 1 n a 21 a 22 … a 2 n a 31 a 32 … a 3 n ⋮ ⋮ ⋮ ⋮ a m 1 a m 2 … a m n m × n Each a i j ( i = 1 , 2 , … m ; j = 1 , 2 , 3 … n ) entry is called the element of the matrix and it is the j t h element of the i t h row Now, matrix of order 2 × 2 is a matrix of 2 rows and 2 column. For example: 1 2 3 4 2 × 2 .

Give an example of 4 × 2 matrix.

A matrix is a rectangular array of numbers (any system of numbers), arranged in rows and columns. If there are m rows, and n columns in a matrix, it is called a matrix of order m × n , and it is given as follows: A = a 11 a 12 … a 1 n a 21 a 22 … a 2 n a 31 a 32 … a 3 n ⋮ ⋮ ⋮ ⋮ a m 1 a m 2 … a m n m × n Each a i j ( i = 1 , 2 , … m ; j = 1 , 2 , 3 … n ) entry is called the element of the matrix and it is the j t h element of the i t h row Now, matrix of order 4 × 2 is a matrix of 4 rows and 2 columns. For example: 1 2 3 4 5 6 7 8 4 × 2 .

Give an example of 1 × 3 matrix.

A matrix is a rectangular array of numbers (any system of numbers), arranged in rows and columns. If there are m rows, and n columns in a matrix, it is called a matrix of order m × n , and it is given as follows: A = a 11 a 12 … a 1 n a 21 a 22 … a 2 n a 31 a 32 … a 3 n ⋮ ⋮ ⋮ ⋮ a m 1 a m 2 … a m n m × n Each a i j ( i = 1 , 2 , … m ; j = 1 , 2 , 3 … n ) entry is called the element of the matrix and it is the j t h element of the i t h row Now, matrix of order 1 × 3 is a matrix of 1 row and 3 columns. For example: 4 7 5 1 × 3 .

Let A = 1 2 3 4 1 4 5 6 1 2 3 9 1 1 6 , what is the order of A ?

Given, A = 1 2 3 4 1 4 5 6 1 2 3 9 1 1 6 We know that A rectangular array of numbers, symbols, or expressions, arranged in rows and columns is a matrix. And, If there are m rows, and n columns in a matrix, it is called a matrix of order m × n . The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively. Clearly, in the given matrix A there are 3 rows, and 5 columns. Hence, the order of matrix A is 3 × 5 .

Let A = 1 2 3 4 1 4 5 6 1 2 3 9 1 1 6 . Write down the entries a 31 , a 25 , a 23 .

A matrix is a rectangular array of numbers (any system of numbers), arranged in rows and columns. If there are m rows, and n columns in a matrix, it is called a matrix of order m × n , and it is given as follows: A = a 11 a 12 … a 1 n a 21 a 22 … a 2 n a 31 a 32 … a 3 n ⋮ ⋮ ⋮ ⋮ a m 1 a m 2 … a m n m × n Each a i j ( i = 1 , 2 , … m ; j = 1 , 2 , 3 … n ) entry is called the element of the matrix and it is the j t h element of the i t h row Here, A = 1 2 3 4 1 4 5 6 1 2 3 9 1 1 6 , Since a 31 denotes the element of third row and first column. ∴ a 31 = 3 . a 25 denotes the element of second row and fifth column. ∴ a 25 = 2 And, a 23 denotes the element of second row and third column. ∴ a 23 = 6 .

Let A = 1 2 3 4 1 4 5 6 1 2 3 9 1 1 6 . Write down A T .

Given matrix is A = 1 2 3 4 1 4 5 6 1 2 3 9 1 1 6 . We know that the transpose of a matrix A is the matrix, obtained from A by changing its rows into columns, and columns into rows. It is denoted by A ' or A T . Thus, if order of matrix A is m × n then order of A ' is n × m . Hence, transpose of the given matrix A is given by A T = 1 4 3 2 5 9 3 6 1 4 1 1 1 2 6 , and it is of order 5 × 3