# Types of Matrices

#### Topics

• ##### Complex Numbers
• Review of Complex Numbers‐Algebra of Complex Number
• Different Representations of a Complex Number and Other Definitions
• D’Moivre’S Theorem
• Powers and Roots of Exponential Function
• Powers and Roots of Trigonometric Functions
• Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ
• Expansion of sinnθ, cosnθ in powers of sinθ, cosθ
• .Circular Functions of Complex Number
• Hyperbolic functions of complex number
• Inverse Circular Functions
• Inverse Hyperbolic Functions
• Separation of Real and Imaginary Parts of All Types of Functions
• ##### Successive Differentiation
• Successive Differentiation
• nth Derivative of Standard Functions
• Leibnitz’S Theorem (Without Proof) and Problems
• ##### Logarithm of Complex Numbers
• Logarithmic Functions
• Separation of Real and Imaginary Parts of Logarithmic Functions
• ##### Matrices
• Inverse of a Matrix
• Addition of a Matrix
• Multiplication of a Matrix
• Transpose of a Matrix
• Types of Matrices
• Rank of a Matrix Using Echelon Forms
• Reduction to Normal Form
• PAQ in normal form
• System of Homogeneous and Non – Homogeneous Equations
• consistency and solutions of homogeneous and non – homogeneous equations
• Linear Dependent and Independent Vectors
• Application of Inverse of a Matrix to Coding Theory
• ##### Partial Differentiation
• Partial Derivatives of First and Higher Order
• Total Differentials
• Differentiation of Composite Functions
• Differentiation of Implicit Functions
• Euler’s Theorem on Homogeneous functions with two and three independent variables (with proof)
• Deductions from Euler’S Theorem
• ##### Applications of Partial Differentiation , Expansion of Functions
• Maxima and Minima of a Function of Two Independent Variables
• Jacobian
• Taylor’S Theorem (Statement Only)
• Taylor’S Series Method
• Maclaurin’s series (Statement only)
• Expansion of 𝑒^𝑥 , sin(x), cos(x), tan(x), sinh(x), cosh(x), tanh(x), log(1+x), 𝑠𝑖𝑛−1 (𝑥),𝑐𝑜𝑠−1 (𝑥),𝑡𝑎𝑛−1 (𝑥)
• Binomial Series
• ##### Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations
• Indeterminate Forms
• L‐ Hospital Rule
• Problems Involving Series
• Solution of Transcendental Equations
• Solution by Newton Raphson Method
• Regula – Falsi Equation
• Solution of System of Linear Algebraic Equations by Gauss Elimination Method
• Gauss Jacobi Iteration Method
• Gauss Seidal Iteration Method
• Row Matrix
• Column Matrix
• Zero or Null matrix
• Square Matrix
• Diagonal Matrix
• Scalar Matrix
• Unit or Identity Matrix
• Upper Triangular Matrix
• Lower Triangular Matrix
• Triangular Matrix
• Symmetric Matrix
• Skew-Symmetric Matrix
• Determinant of a Matrix
• Singular Matrix
• Transpose of a Matrix
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Matrices class 12 part 6 (Row and column Matrices) [00:04:07]
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