Archive for February 2016
Matrix Algebra: Ba/Bsc students
Addition And Subtraction Of Matrix:
Two matrices can be added or subtracted only if they have the same order. It means the matrices must have the same number of rows and columns.
Addition and subtraction is done by adding or subtracting the corresponding elements. For example, A and B are two matrices below:
Tag :
Economics,
mathematics,
Matrix Algebra : Transpose of a matrix
Transpose of a matrix:
Transpose of a matrix is obtained by interchanging rows and columns of a matrix. For example if a matrix is:
Then transpose of the above matrix will be
When we transpose a matrix then the order of matrix changes, but for a square matrix order remains same.
Tag :
Economics,
mathematics,
Matrix algebra
Level: BA/Bsc
Subject: mathematical economics
Types of Matrices:
Column matrix:
A matrix is said to be a column matrix if it has only one column. For example, below is a column matrix of order 3×1
Row matrix:
A matrix is said to be a row matrix of it has only one row. For example , below is a row matrix of order 3×1
Square matrix:
A matrix is said to be a square matrix if its number of rows are equal to the number if its columns. Thus m×n matrix is said to be a square matrix if m=n and is known as a square matrix of order 'n' . For example:
Matrix A is a square matrix of order 2
While, matrix B is a square matrix of order 3.
Equal matrix:
Two matrix are equal if their corresponding elements are equal. If two matrices fulfill the following conditions, they are said to be equal:
- Each matrix has the same number of rows.
- Each matrix aphas the same number of columns.
- Corresponding elements within each matrix are equal.
Consider the three matrices shown below.
If A=B , we know that x=3 and y=0; since corresponding elements of equal matrices are also equal. And we know that the matrix C is not equal to A or B because C has more columns than A or B.
Diagonal matrix:
A square matrix is said to be a diagonal matrix if all its non diagonal elements are zero. For example,
Scalar Matrix:
A diagonal matrix is said to be a scalar matrix if its diagonal elemennts are equal. For example,
are scalar matrices of order 2 and 3, respectively.
Identity matrix:
A square matrix in which elements in the diagonal are all 1 and rest of the elements are all zero is called an identity or unit matrix.
For example,
Note:
A scalar matrix is an identity matrix when k=1. But every identity matrix is clearly a scalar matrix. The identity matrix has a unique feature that ifbanmatrix that is multiplied by identity matrix remains the same; that is: AI=IA=A
Null matrix:
A matrix is said to be zero matrix or null matrix if all its elements are zero.
For example,
Tag :
Economics,
Matrix Algebra
Matrix Algebra
Level: B.A/Bsc
Subject : Mathematical economics
Matrices are one of the most important tools which is used not only to mention the coefficients in the system of linear equations but also used to solve the problems of input-output model in economics.
A matrix is simply a set of numbers arranged in rows and columns in a rectangular table.
This is an example of 3×3 matrix. The numbers of rows and columns that a matrix has is called its dimensions or its order. Thus we can say that the dimension (or order) of the above matrix is 3×3. We usually write matrices inside brackets [ ].
Numbers that appear in rows and columns of a matrix are called elements of the matrix. Columns are vertical while rows are horizontal. In the above image the first element of the first column is 1 ..second element of the first column is 2 and third element of the first column is 3.. While the first element of the second column is 2 and so on..
There are 8 types of matrices in mathematical economics:
- Column matrix
- Row matrix
- Square matrix
- Equal matrix
- Diagonal matrix
- Scalar matrix
- Identity matrix
- Null matrix
Tag :
Economics,
