4 8 Non Homogeneous Systems – Class 11TH Math

4.8 System of Non-Homogeneous Linear Equations

Three linear equations in three variables such as:

\begin{align*} a_1x + b_1y + c_1z &= d_1 \\ a_2x + b_2y + c_2z &= d_2 \\ a_3x + b_3y + c_3z &= d_3 \end{align*}

is called a system of non-homogeneous linear equations in the three variables $x, y$ and $z$ , if constant terms $d_1, d_2$ and $d_3$ are not all zero.

Consistent: A system of linear equations is said to be consistent if the system has a unique solution or it has infinitely many solutions.
Inconsistent: A system of linear equations is said to be inconsistent if the system has no solution.

Now we will solve the system of non-homogeneous linear equations with the help of the following methods:

(i) Using reduced echelon form
(ii) Using matrix inversion method
(iii) Using Cramer's rule

4.8 System of Non-Homogeneous Linear Equations

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