Sharma Academy

Home
Subject
Maths
About Us

Search This Blog

Linear Equation by Cramer's Rule

May 24, 2018

Comments

Relation between Normal Matrix and Identity Matrix

Video Lecture We know that any number remains the same when multiplied by 1. e.g. : Similarly, any matrix remains the same when multiplied by the identity matrix. e.g. : ; where , A is a matrix I is a identity matrix Note : Identity matrix is a square matrix whose diagonal element is 1 and remaining element are zero's . e.g. :

Inverse Matrix and Invertible Matrix

Video Lecture If A is a square matrix of order m , and if there exists another square matrix B of the same order m , such that AB = BA = I , then B is called the inverse matrix of A and it is denoted by . In that case A is said to be invertible matrix. e.g. : Let Thus B is the inverse of A , in other words and A is inverse of B i.e.,

Matrix as a Sum of Symmetric Matrix and Skew-Symmetric Matrix

Video Lecture Every square matrix is uniquely expressible as the sum of a Symmetric matrix and a Skew- Symmetric matrix . Let A = P + Q , where P is Symmetric and Q is Skew-Symmetric. ∴ A ' = ( P + Q ) ' = P ' + Q ' = P + ( - Q ) = P - Q . solving , we get ∴ Representation of A as the sum

Powered by Blogger

Linear Equation by Cramer's Rule

Comments

Post a Comment