What are Matrices and Determinants | Types of Matrices
written by Azhar EjazA rectangular array of numbers enclosed by a pair of brackets is called a matrix.
Example:
The number used in rows and columns is said to be entries or elements of the matrix.
Order of Matrices
The number of rows and columns in a matrix is called the order of the matrix. If a matrix B has ‘m’ rows and ‘n’ columns, its order will be ‘m x n’.
Types of matrices
There are different types of matrices.
1. Row Matrix:
A matrix having one row is called a row matrix.
2. Column Matrix
A matrix having one column is called a column matrix.
3. Square Matrix:
A matrix having an equal number of rows and columns is called a square matrix.
4. Rectangular Matrix:
A matrix in which the number of rows are not equal to the number of columns.
5. Diagonal Matrix:
A square matrix ‘A’ is said to be diagonal if all of its off-diagonal elements are zero and at least one of the diagonal elements is non-zero
6. Scalar Matrix:
A square matrix ‘A’ is said to be a scalar matrix if all of its off-diagonal elements are zero and all elements in the leading diagonal are the same non-zero scalar.
7. Unit Matrix:
A square matrix is said to be a unit or identity matrix if all of its off-diagonal elements are zero and all elements in the leading diagonal are ‘1’.
8. Null or Zero Matrix:
A square or rectangular matrix whose each element is zero is called a null or zero matrices.
9. Equal matrices:
Two matrices A and B are said to be equal if,
1. The order of A and B are the same.
2. The corresponding entries in A and B are the same.
Determinant:
The determinant of a square matrix A of order n is the sum of the products of each element of a row (or column) and its corresponding co-factors. It is represented by, |A|.
How do find determinants?
Finding determinant for 2×2 order
Finding determinant for 3 x 3 order.
Frequently Asked Question-FAQs
what is Matrix ?
A matrix is a rectangular arrangement of a collection of numbers into a fixed number of rows and columns. When the elements are arranged in a matrix horizontally, it forms the rows of a matrix. When the elements are arranged in a matrix vertically, it forms the columns of a matrix.
what is a Matrix used for?
Matrices can be used for a variety of purposes in different fields, including engineering, physics, economics, statistics, and mathematics. They also have important applications in computer graphics, where they can be used to represent rotations and other transformations of images.
What is Order of Matrix?
A system of representing the number of rows and columns of a matrix in mathematical form is called the order of a matrix.
who is Father of Matrices?
The matrix is a mathematical concept that was first introduced by Arthur Cayley in his Memoir on the Theory of Matrices. He is therefore considered to be the father of matrices. In his work, he defined the matrix as a rectangular array of numbers that can be used to represent linear transformations.
what is Matrix in Real Life?
Matrices are used extensively in the field of geology for seismic surveys, graphing, statistical analysis, and scientific research. They have a broad range of applications and can be useful in many different fields.
What is Determinant?
The determinant of a square matrix A of order n is the sum of the products of each element of a row (or column) and its corresponding co-factors. It is represented by, |A|.
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