Scalar Multiplication of Matrices

What are Matrix Operations?

Matrix operations are the operations that are used to combine various matrices to form a single matrix. The operations such as addition, subtraction, and multiplication are easily performed on the matrix. These matrix operations are very useful to solve matrix problems and to find the transpose and the inverse of the matrix....

Addition of Matrices

As we add two numbers we can easily add two matrices. The only thing we have to note is that the order of both the matrices that are to be added must be the same. That is to add two matrices we have to make sure that they are of the same order and then each element of the first matrix adds with each element of the second matrix to get a single matrix and thus the addition operation gets completed....

Subtraction of Matrices

As we add two matrices e can also easily subtract two matrices. The only thing we have to note is that the order of both the matrices that are to be subtracted must be the same. That is to subtract two matrices we have to make sure that they are of the same order and then each element of the first matrix is subtracted with each element of the second matrix to get a single matrix and thus the subtraction operation gets completed....

Scalar Multiplication of Matrices

For any matrix A = [aij]m×n if we multiply the matrix A with any scaler (say k) then the scaler is multiplied by each element of the matrix and this is called the scalar multiplication of matrices....

Multiplication of Matrix

Matrix multiplication is the operation that helps us to multiply two matrices. This is different from algebraic multiplication and not all the matrices can be multiplied. Only those matrices can be multiplied where the number of columns in the first is equal to the number of rows in the second, i.e for matrix Am×n and matrix Bn×p the multiplication is possible for any other matrices where the column of the first matrix is not equal to the row in the second matrix the multiplication is not possible....

Transpose Operation of a Matrix

Tramspose operation of a matrix is used to find the transpose of any matrix. Transpose of any matrix is a matrix in which the rows of the matrix are changed to the column of the matrix and the column of the matrix is changed to the rows of the matrix. Suppose we have a matrix A of order m×n such that A =[ij]m×n then the transpose of matrix A is represented as (A)T and its value is,...

Inverse Operation of a Matrix

For any matrix A its inverse is found only when A is a square matrix and its determinant is equal to 1, i.e....

Solved Examples on Matrix Operations

Example 1: Find the sum of matrix A and B when,...

FAQs on Matrix Operation

What Product of a Matrix with an Identity Matrix?...