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 matrix form? Well, in the matrix form, it will be …
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 the original matrix. Now I give an example. Let’s say…
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 that.e a set of equations in matrix algebra like Gaussian…
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 the denominator is . Also the numerator is . So, I can say that the degree of…
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 have a step function First of all, I’ll write it…
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 of Since is a product of two functions, I’ll use the product…
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 an example of second-order homogeneous difference equations. Now I’ll show…
First-Order Homogeneous Ode
WHAT IS A FIRST-ORDER HOMOGENEOUS ODE? Now any differential equation with is a first-order ODE. This type of equation does not have any higher-order derivative. Next is ‘homogeneous.’ Now any first-order ODE…
Gauss-Jordan Method To Find Out The Inverse Of A Matrix
Let’s say I have a matrix And I want to find out the inverse of this matrix. Now, to get the inverse of the matrix , I will follow a few…
First-Order Partial Derivative Of Functions With Three Variables
EXAMPLE 1 According to Stroud and Booth (2013)* “If express in its simplest form SOLUTION Here the given function is And, I have to find out the value of So I’ll…
