Matrices

Matrices and Their Types

•    A matrix is an ordered rectangular array of numbers or functions arranged in rows and columns. A matrix having m rows and n columns is called a matrix of order m x n. In general, an m × n matrix is represented as below:

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Operations on Matrices

•    Let A = [aij] m x n and B = [bij] m x n be two matrices of same order m x n. Then the sum of the two matrices A and B is defined as a matrix
C = [cij] m x n  where cij = aij + bij   for all possible values of i and j.

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Inverse of a Matrix

•    Inverse of a square matrix is same as the reciprocal of a number. Inverse of square matrix A is denoted as A–1.

•    Product of a square matrix and its inverse is always a identity matrix of the same order that is AA–1 = I.

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Martin's Rule

  • Basic application of matrix is to solve a system of linear equations. If a system of linear equations has one or more solutions, it is said to be consistent.  
  • A square matrix A is invertible if and only if A is a non-singular matrix, i.e., |A| ≠ 0. Inverse of a non-sin .... Read More

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