Introduction to Three–dimensional Geometry

Symmetric & Skew Symmetric Matrix-Properties, Solved Examples, Class 12 Matrices Chapter Notes Study Material Download pdf

A symmetric matrix and skew-symmetric matrix both are square matrices. But the difference between them is, the symmetric matrix is equal to its transpose whereas skew-symmetric matrix is a matrix whose transpose is equal to its negative. If A is a symmetric matrix, then A = A T and if A is a skew-symmetric matrix then A T = – A. Table of Contents Symmetric Matrix Properties of Symmetric Matrix Skew Symmetric Matrix Properties of Skew Symmetric Matrix Determinant of Skew Symmetric Matrix Eigenvalue of Skew Symmetric Matrix Frequently Asked Questions-FAQs What is a symmetric matrix? How do you know if a matrix is symmetric? Give an Example of a Matrix Which is Symmetric but not Invertible. Is Symmetric Matrix Diagonalizable? What is skew-symmetric matrix? What is the difference between symmetric and skew-symmetric matrix? Symmetric Matrix To understand if a matrix is a symmetric matrix, it is very important to know about transpose of a matrix and how to find it. If we in...

Transpose of a Matrix-Addition & Multiplication Property of Transpose, Solved Examples, Class 12 Matrices Chapter Notes Study Material Download pdf

Transpose of a matrix is one of the most commonly used methods in matrix transformation. For a given matrix, the transpose of a matrix is obtained by interchanging rows into columns or columns to rows. In this article, we are going to learn the definition of the transpose of a matrix, steps to find the transpose of a matrix, properties and examples with a complete explanation. Before learning how to find the transpose of a matrix, first let us learn, what a matrix is? Table of Contents What is a Matrix? Transpose of a Matrix Definition How to Find the Transpose of a Matrix? Properties of Transpose of a Matrix (i) Transpose of the Transpose Matrix (ii) Addition Property of Transpose (iii) Multiplication by Constant (iv) Multiplication Property of Transpose Transpose of a Matrix Examples Practice Problems Frequently Asked Questions What is the transpose of a matrix? How to calculate the transpose of a Matrix? What is the Addition Property of Transpose? What is the Multiplication Property...

Classification of Drugs-Chemistry in Everyday Life Class 12 Notes and Study Material

Chemistry plays an extremely vital role in everyday life. The principles of chemistry have benefited human life on a massive scale though we sometimes tend to overlook them. All textiles are processed by chemicals. Our clothes, some of them completely synthetic, involve processes, chemicals, dyes, and fibers. Consider cleanliness. Our household is filled with detergents, soaps, bleaches, kinds of toothpaste, etc. Moreover, even the food that we consume every day has several chemicals involved. Electronic materials, fuels, explosives, rocket propellants, building materials, etc., are all considered chemicals. Daily lives have been influenced by chemistry so much that one does not even realize that people come across chemicals at every moment; that humans themselves are beautiful chemical creations and all the activities are controlled by chemicals. Even in sickness and diseases, people resort to medicines, again chemicals. Table of Contents What are Drugs ? Classification Of Drugs Conce...

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