Master The Basics Of Matrices: Types, Operations, And Applications

Matrix

A rectangular array of numbers

Matrix is a rectangular array of numbers, symbols or expressions arranged in rows and columns. A matrix is a useful mathematical tool in various fields such as economics, physics, engineering, computer science, and statistics.

A matrix can be represented as [A] where ‘A’ is a rectangular array of numbers.

Types of matrices:
1. Square Matrix: It is a matrix which has the same number of rows and columns.
2. Row Matrix: A matrix which has only one row is called a row matrix.
3. Column Matrix: A matrix which has only one column is called a column matrix.
4. Zero Matrix: A matrix having all its elements as zero is called a zero matrix.
5. Identity Matrix: A square matrix having 1 in the diagonal and all other elements as zero is called an identity matrix.
6. Diagonal Matrix: A matrix which has elements only in the diagonal and all other elements as zero is called a diagonal matrix.

Operations on matrices:
1. Addition: Two matrices can be added if they have the same dimensions.
2. Subtraction: Two matrices can be subtracted if they have the same dimensions.
3. Multiplication: Two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix.
4. Transpose: The transpose of a matrix is obtained by interchanging its rows and columns.

Applications of matrices:
1. Linear equations: Matrices can be used to solve systems of linear equations.
2. Computer graphics: Matrices are used to represent the position, orientation, and size of graphics objects in computer graphics.
3. Quantum mechanics: Matrices are used to describe the state of quantum mechanical systems.
4. Markov process: Matrices are used to represent Markov processes in probability theory.

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