Gravitation Class 11 Notes

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...

Onto Functions(Surjective Functions)-Definition, Graph, Properties, Solved Examples, FAQs

Onto Function is one of the many types of functions defined based on the relationship between its domain and codomain. For any function to be onto, it needs to relate two sets with a very specific mapping between elements, meaning that each element of the codomain has at least one element in the domain as its pre-image. In simple words, for any function, if all the elements of the codomain are mapped to some element of the domain, then the function is said to be an onto function. In this article, we will discuss the concept of onto or surjective function in detail including its definition, example, and many more. We will also discuss key differences between one one, onto and into functions as well. Table of Contents What is an Onto Function? Onto Function Definition Representation for Onto Function Examples of Onto Function Properties of Onto Function Composition of Onto Function Onto Function Graph Number of Onto Functions One to One and Onto Functions Onto and Into Functi...

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...

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