In every question of 12th Maths Chapter 3 Matrix, the explanation of each step is given. The step by step solutions for plus two Maths is given with video solution and PDF file format. We will definitely rectify.
The arrangement of real numbers in a rectangular array enclosed in brackets as [] or is known as a Matrix Matrices is plural of matrix. Matrix operations are used in electronic physics, computers, budgeting, cost estimation, analysis and experiments.
They are also used in cryptography, modern psychology, genetics, industrial management etc. In general an m x n matrix is matrix having m rows and n columns. There may be any number of rows and any number of columns in a matrix. If there are m rows and n columns in matrix A, its order is m x n and it is read as an m x n matrix. Theorems of invertible matrices. Matrix is a latin word. Originally matrices are used for solutions of simultaneous linear equations.
Carl Friedrich Gauss � also gave the method to solve simultaneous equations by matrix method. Matrix The arrangement of real numbers in a rectangular array enclosed in brackets as [] or is known as a Matrix Matrices is plural of matrix.
Order of a Matrix There may be any number of rows and any number of columns in a matrix. Types of Matrices Row matrix: A row matrix has only one row but any number of columns.
Column matrix: A column matrix has only one column but any number of rows. Square matrix: A square matrix has the number of column equal to the number of rows. Rectangular Matrix: A matrix is said to be a rectangular matrix if the number of rows is not equal to the number of columns. Diagonal matrix: If in a square matrix has all elements 0 except principal diagonal elements, it is called diagonal matrix. Scalar Matrix: A diagonal matrix is said to be a scalar matrix if all the elements in its principal diagonal are equal to some non-zero constant.
Zero or Null matrix: If all elements of a matrix are zero, then the matrix is known as zero matrix and denoted by O. Unit or Identity matrix: If in a square matrix has all elements 0 and each diagonal elements are non-zero, it is called identity matrix and denoted by I. Equal Matrices: Two matrices are said to be equal if they are of the same order and if their corresponding elements are equal.
Properties of Matrices When a matrix is multiplied by a scalar, then each of its element is multiplied by the same scalar. Additive identity is a zero matrix, which when added to a given matrix, gives the same given matrix, i.
If A and B are two matrices of order m x p and p x n respectively, then their product will be a matrix C of order m x n. Theorems of invertible matrices Theorem 1: Every invertible matrix possesses a unique inverse. Theorem 2: A square matrix is invertible iff it is non-singular. Historical Facts!
Important Questions on 12th Maths Chapter 3 If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements? Determinants �.
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