Explain matrices and its type with example?
Answers
in order to range numerous numbers, mathematics provides a simple solution: matrices. A matrix can be defined as a rectangular grid of numbers, symbols, and expressions arranged in rows and columns. These grids are usually charted by brackets around them.
The dimensions of a matrix are represented as R X C, where R is the number of rows and C is the number of columns. This R X C notation is also called the order of the matrix.
Types of Matrices
There are various types of matrices, depending on their structure. Let's explore the most common types:
Null Matrix
A matrix that has all 0 elements is called a null matrix. It can be of any order. For example, we could have a null matrix of the order 2 X 3. It's also a singular matrix, since it does not have an inverse and its determinant is 0.
Null Matrix
Any matrix that does have an inverse can be called a regular matrix.
Row Matrix
A row matrix is a matrix with only one row. Its order would be 1 X C, where C is the number of columns. For example, here's a row matrix of the order 1 X 5:
Row Matrix
Column Matrix
A column matrix is a matrix with only one column. It is represented by an order of R X 1, where R is the number of rows. Here's a column matrix of the order 3 X 1:
Column Matrix
Square Matrix
A matrix where the number of rows is equal to the number of columns is called a square matrix. Here's a square matrix of the order 2 X 2:
Square Matrix
Diagonal Matrix
A diagonal matrix is a square matrix where all the elements are 0 except for those in the diagonal from the top left corner to the bottom right corner. Let's take a look at a diagonal matrix of order 4 X 4:
Diagonal Matrix
A special type of diagonal matrix, where all the diagonal elements are equal is called a scalar matrix. We can see a 3 X 3 scalar matrix here:
Scalar Matrix
A scalar matrix whose diagonal elements are all 1 is called a unit matrix, or identity matrix.
Unit Matrix
Upper Triangular Matrix
A square matrix where all the elements below the left-right diagonal are 0 is called an upper triangular matrix. Here's an upper triangular matrix of order 3 X 3:
Upper Triangular Matrix
Lower Triangular Matrix
A square matrix where all the elements above the left-right diagonal are 0 is called a lower triangular matrix. Here's what a lower triangular matrix of order 3 X 3 could look like:
Lower Triangular Matrix
Symmetric Matrix
A matrix whose transpose is the same as the original matrix is called a symmetric matrix. Only a square matrix can be a symmetric matrix. The transpose of a matrix is another matrix that is formed by switching the rows and columns of a given matrix. The given matrix A is a 3 X 3 symmetric matrix, since it's the same as its transpose AT.
Symmetric Matrix A matrix whose transpose is the same as the original matrix is called a symmetric matrix. Only a square matrix can be a symmetric matrix. The transpose of a matrix is another matrix that is formed by switching the rows and columns of a given matrix. The given matrix A is a 3 X 3 symmetric matrix, since it's the same as its transpose AT.