Conclusion – System of Linear Equations

System of Linear Equations

A system of linear equations is a mathematical concept involving two or more linear equations that 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 be 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:...

Properties of Rank of a Matrix

If A is a null matrix then P(A) = 0 i.e. Rank of null matrix is zero. If In is the nxn unit matrix then P(A) = n. Rank of a matrix A mxn , P(A) ? min(m,n). Thus P(A) ?m and P(A) ? n. P(A nxn ) = n if |A| ? 0 If P(A) = m and P(B)=n then P(AB) ? min(m,n). If A and B are square matrices of order n then P(AB) = P(A) + P(B) – n. If Am×1 is a non zero column matrix and B1×n is a non zero row matrix then P(AB) = 1. The rank of a skew symmetric matrix cannot be equal to one....

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....

Applications in Engineering

Systems of linear equations are widely used in various engineering disciplines:...

Conclusion – System of Linear Equations

Understanding and solving systems of linear equations are crucial skills in engineering and many other fields. Various methods, including graphical, substitution, elimination, and matrix methods, provide versatile tools for finding solutions. The applications of these systems are vast and integral to solving complex real-world problems....

FAQs on System of Linear Equations

What is a system of linear equations?...