## Order of matrix in Discrete mathematicsWe can show the number of rows and columns of any matrix with the help of order of that matrix. A matrix can be described as an array of elements that are arranged in the form of rows and columns. With the help of order of matrix, we will be able to get the count of rows and columns in the given matrix. The order of matrix is also known as the dimension of matrix. It is expressed in the form of a number of rows multiplied by the number of columns, and we can read the order of matrix as the number of rows by the number of columns. When we multiply the number of rows and columns of any matrix, then we will be able to get the number of elements of that matrix. Further, we can get the types of matrix with the help order of the matrix. It can also provide us the total number of elements that are present in any matrix. The elements of the matrix are arranged in the form of m rows and n columns. We will be able to decide whether the particular arithmetic operation will be performed on the two matrices with the help of order of the matrix. It is used to know about the different types of matrices. We can also learn about the different types of arithmetic operations that will be performed on these matrices. In this section, we will learn about the order of matrix, types of matrices on the basis of order of the matrix, Different matrix operations, examples of order of a matrix, and many more things. ## What is Order of matrixWe will get the dimension of a matrix with the help of order of the matrix. The dimension of matrix is used to show the number of rows and a number of columns in the matrix. The symbol A If there is any order of a matrix, then the first number of the order will always be used to indicate the rows, and the second number of the order will be used to indicate the columns. In this image, we can see that the number of rows is m, and the number of columns is n. ## Examples of matrices on the basis of orderHere we will show some matrices with different orders and the total number of elements in the given matrix, which are described as follows:
A = [-6] In this matrix, we can see that there is 1 row and 1 column in matrix A. We can read this matrix as one by one matrix. That's why matrix A will be known as the matrix of order 1*1. In the above matrix A, the total number of elements = 1*1 = 1.
B = [2 6 7] In this matrix, we can see that there are 1 row and 3 columns in matrix B. We can read this matrix as one by three matrix. That's why matrix B will be known as the matrix of order 1*3. In the above matrix B, the total number of elements = 1*3 = 3.
In this matrix, we can see that there are 2 rows and 2 columns in matrix C. That's why matrix C will be known as the matrix of order 2*2. We can read this matrix as two by two matrix. We can simply call it a matrix of order 2. In the above matrix C, the total number of elements = 2*2 = 4.
In this matrix, we can see that there are 3 rows and 4 columns in matrix B. We can read this matrix as three by four matrix. That's why matrix B will be known as the matrix of order 3*4. In the above matrix B, the total number of elements = 3*4 = 12. ## Types of matrices on the basis of order of matrixWe can get the dimensions of the matrix with the help of order of the matrix. There are different types of matrices, and we can find the order of these matrices. Some different types of matrices with their orders are described as follows:
A _{1*n} = [a1 a2& a3 … an]
## Order of matrix for Different matrix operationsOn the basis of the types of matrices, the order of the matrices depends. There are a lot of operations of matrices that are also based on the order of matrix. Now we will see some operations on matrices, and we will perform them on the basis of order of the matrix. These operations are described as follows:
In this example, we can see that matrix A contains an order 2*3, and matrix B contains an order 2*3. That means both matrices have the same order. Se we will add the corresponding elements of matrix A and matrix B and get a matrix as a result with the same order 2*3.
In this example, we have two matrices in which the number of columns in the 1 ## Important notes on Order of matrixThere are some points that we should know when we learn about the order of matrix, which is described as follows: - Suppose there is a matrix that contains an order m*n. Here the first number, m will always be used to indicate the number of rows, and another number, n will be used to indicate the number of columns.
- If we want to add or subtract two matrices, for this, the order of these matrices must be similar to each other.
- If we want to perform the multiplication of two matrices, in this case, the number of columns in 1
^{st}matrix and the number of rows in the 2^{nd}matrix must be similar to each other. - When we do the multiplication of two matrices, then we will get a resultant matrix with the order where the number of rows will be similar to the 1
^{st}matrix, and the number of columns will be similar to the 2^{nd}
## Examples of Order of matrixThere are various examples of order of the matrix, and some of them are described as follows:
If we want to perform matrix multiplication on two matrices, then the number of columns in the 1 A As we can see, we get C as a result of the multiplication of matrices A and B. The matrix C has the number of rows of the 1 Answer: Therefore, the second matrix can have an order 3*2, and the resultant matrix can have an order 4*2.
The first condition of matrix multiplication is satisfied by these matrices, which say that the number of columns of the 1 Further, the order of a resultant matrix must have the number of rows of the 1 A Answer: Therefore, the resultant matrix will have the order 2*3.
But the order of matrix A is 3*4, and the order of matrix B is 4*3, which are not equal to each other. So it is not possible to add matrices A and B. Answer: A+B is not possible. Next TopicHermitian matrix in Discrete mathematics |