Trace of a matrix

System of Linear Equations

A system of linear equations is a mathematical concept involving two or more equations that are linear in nature and share the same variables. These equations collectively define relationships between variables, often representing lines, planes, or higher-dimensional surfaces in space. The solution to the system is the set of values for the variables that satisfies all equations simultaneously, typically corresponding to points of intersection or commonality among the equations....

Trace of a matrix

Let A=[aij] nxn is a square matrix of order n, then the sum of diagonal elements is called the trace of a matrix which is denoted by tr(A). tr(A) = a11 + a22 + a33+ ……….+ ann...

Properties of a trace of the matrix:

Let A and B be any two square matrices of order n, then...

Solution of a system of linear equation

Linear equations can have three kinds of possible solutions:...

How to Solve System of Linear Equations?

The subsequent techniques for solving the system of linear equations AX = B are viable solely under the condition that the coefficient matrix A is non-singular, meaning |A| ≠ 0....