basic 3 min read
Matrix Inverse
This lesson defines the matrix inverse, and shows how to determine whether the inverse of a matrix exists. Matrix Inversion Suppose A is an n x n matrix.…
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basic 2 min read
Algebra of Matrices
Algebra of Matrices is the branch of mathematics, which deals with the vector spaces between different dimensions. The innovation of matrix…
basic 2 min read
Curl Of A Vector Function
Suppose I have a vector such as . Now the curl of this vector will be So if I evaluate the determinant, I’ll get…
basic 1 min read
Divergence Of A Vector Function
Suppose I have a vector such as . Now the divergence of this vector will be So if I use the technique for first-order…
basic 3 min read
The Line Integral Of A Scalar Field
EXAMPLE 1 According to Stroud and Booth (2011),* “If , evaluate between and along the curve with parametric equations .” SOLUTION Here the given scalar field…
basic 3 min read
Gaussian Elimination Method In 3 × 3 Matrices
Suppose I have a system of equations like How it would be if I want to write it in a…
basic 3 min read
Symmetric, Skew-Symmetric And Orthogonal Matrices
Suppose I have a matrix . Then the matrix will be symmetric if the transpose of the matrix is the same as…
basic 5 min read
Triangular Decomposition Method In 3 × 3 Matrices
There are several ways to solvrow transformation method, inverse matrix method and so on. The triangular decomposition method is also one of…
basic 2 min read
Partial Fractions Of Higher Degree Numerators With Examples
EXAMPLE 1 Write the following expression into the partial fraction form: . SOLUTION Here the given expression is: . That means…
basic 2 min read
Laplace Transform Of A Unit Step Function
EXAMPLE 1 According to Stroud and Booth (2011)*, “A function is defined by ….determine its Laplace transform.” SOLUTION Now here I…
basic 1 min read
Product Rule Of Differentiation
Suppose is a product of two functions and . This means Now my task is to differentiate , that is, to get the value…
basic 3 min read
Homogeneous Difference Equations
Now the general form of any second-order difference equation is: Also, are constants. If , then the equation becomes Then this is…
