Matrices: Types of Matrices and Determinant of Matrix Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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What Are Matrices?

  • Matrices are an important branch of mathematics, which also helps students understand other mathematical concepts due to the interrelatedness to other branches. A matrix can be defined as an array of numbers or functions arranged in a rectangular order.
  • In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
  • For example, the dimension of the matrix below is (read β€œtwo by three” ) , because there are two rows and three columns.
  • A matrix which possesses rows titled β€œX” and columns titled as β€œY” is called as a matrix of an order of . The major operations carried out with Matrices are the Addition, Subtraction, and Multiplication. Understanding the types of matrices is essential to understand, the other topics better.

Types of Matrices

The Image Og Matrix Classification

Matrices are commonly classified into:

  • Column Matrix:- A matrix which consists of a singular column can be defined as a column matrix.
    • For Example:
  • Row Matrix:- If a matrix has only a singular row, then it is termed as a row matrix
    • For example:
    • Here order of A is and that of B is
  • Square Matrix:- When the number of rows is equal to the number of columns, then the matrix is defined as a square matrix.
    • For Example:

  • Diagonal Matrix:- If the diagonal elements are zero in a square matrix, then it can be defined as a diagonal matrix.
    • For Example: 0

Hence the orders of A, B and C are 1,2 and 3 respectively

  • Scalar Matrix:- When the diagonal elements are equal in a diagonal matrix, then this matrix is assumed to be a Scalar matrix.
    • For Example:

  • Identity Matrix:- An identity matrix can be defined as a square matrix, whose elements in the diagonal are , while the other elements are zero.
    • For Example:

Are identity matrices of order 1,2 and 3 respectively

  • Zero Matrix:- In a matrix, when all the elements are zero, it can simply be defined as a null matrix or a zero matrix.
    • For Example:

  • The orders of the above matrices are and respectively
  • If two square matrices called A and B exist then we can safely assume that , where B is the inverse matrix of A and A is the inverse of B. A square matrix, on the other hand, can be termed as the sum of a skew matrix and a symmetric matrix.

Determinant of Matrix

A determinant of a matrix is the addition of the products of the elements within a square matrix. If are the elements in a matrix.

Then, the determinant is

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