Matrices and Determinants

IMPORTANT

Mathematics Solutions from Chapter -1 - Matrices and Determinants

This chapter covers topics such as Eigenvalues and Characteristic Equation, Properties of Determinants, Adjoint of a Matrix, Algebra of Matrices, Determinant of a Square Matrix, System of Linear Equations, Basics of Matrices, etc.

Practice Other Topics from Matrices and Determinants

This topic covers concepts such as Matrices and Determinants, Matrices, Definition of a Matrix, Rows and Columns of a Matrix, Order of a Matrix, Submatrix of a Matrix, Number of Submatrices of a Matrix, Types of Matrices, Row Matrix, etc.

This topic covers concepts such as Comparable Matrices, Equality of Matrices, Operations on Matrices, Addition of Matrices, Algebraic Properties of Matrix Addition, Condition for Addition of Two Matrices, Closure Property of Matrix Addition, etc.

Mathematics>Algebra>Matrices and Determinants>Symmetric and Skew-symmetric Matrices

This topic covers concepts such as Symmetric and Skew-Symmetric Matrices, Properties of Symmetric Matrices, Properties of Skew-Symmetric Matrices, Square Matrix as a Sum of Symmetric and Skew-Symmetric Matrices, etc.

This topic covers concepts such as Special Types of Matrices, Idempotent Matrix, Periodic Matrix, Nilpotent Matrix, Involuntary Matrix, Orthogonal Matrix, Unitary Matrix, Hermitian and Skew-hermitian Matrices, Hermitian Matrix, etc.

Mathematics>Algebra>Matrices and Determinants>Determinant of a Square Matrix

This topic covers concepts such as Determinant, Determinant of a Square Matrix, Minors and Cofactors, Product of a Row/Column with Cofactors of Another Row/Column, Value (Cofactor Expansion) of a Determinant, Transpose of a Determinant, etc.

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

This topic covers concepts such as Properties of Determinants, Equality of Determinant and Its Transpose, Properties of Determinants under Elementary Transformations, Value of a Determinant Having Identical Rows/Columns, etc.

This topic covers concepts such as Adjoint of a Matrix, Cofactor Matrix, Properties of Adjoint of Matrices, etc.

This topic covers concepts such as Existence of Multiplicative Inverse in Matrices, Cancellation Law in Matrix Multiplication, Inverse of a Matrix, Invertible Matrices, Properties of Inverse of Matrices, Methods to Find Inverse of a Matrix, etc.

Mathematics>Algebra>Matrices and Determinants>System of Linear Equations

This topic covers concepts such as System of Linear Equations, Non-homogeneous System of Linear Equations, Homogeneous System of Linear Equations, Solutions of System of Linear Equations, Consistent and Inconsistent System of Linear Equations, etc.

Mathematics>Algebra>Matrices and Determinants>Eigenvalues and Characteristic Equation

This topic covers concepts such as Inverse of a Matrix Using Given Polynomial Equation, Characteristic Equation (Polynomial) of a Matrix, Eigenvalue of Characteristic Equation of a Matrix, etc.