Class 12 Maths Matrix based System of Linear Equations Notes has been updated according to the latest syllabus of 2080. It means the solutions of Matrix based System of Linear Equations chapter provided in this article contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of this chapter because we are here to serve you.

## Chapter – 5

__Matrix based System of Linear Equations__

We come across equations, when we try to solve some problems in mathematics. These equations may be of one or more variables. The solutions of the equations give the solutions of the problems.

So it is quite natural that we should have knowledge of different methods of solving equations. The methods, we consider here, are row equivalent matrix method, Cramer’s rule or Determinant method and Inverse matrix method.

### Cramer’s Rule

Cramer’s Rule is a method used to solve a system of linear equations using determinants. This rule provides an alternative approach to solving systems of linear equations without the need for matrix inversion. In Class 12 Mathematics, students learn about Cramer’s Rule as a useful technique for solving systems of linear equations with multiple variables.

## Class 12 Maths Matrix based System of Linear Equations PDF

This PDF will provide the solutions of every question from the 2nd exercise of class 12 System of Linear Equations. If you want the solutions of other exercises then you can select the exercise from the button given above.

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### Understanding Cramer’s Rule:

Cramer’s Rule is based on the concept of determinants and involves calculating the determinants of matrices derived from the coefficients of the linear equations. By applying Cramer’s Rule, students can find unique solutions for each variable in the system of equations, provided certain conditions are met.

### Steps to Apply Cramer’s Rule

**Formulate the System of Equations:**Write the given system of linear equations in standard form.**Construct Coefficient Matrices:**Create coefficient matrices by replacing the coefficients of variables with the constants on the right-hand side.**Calculate Determinants:**Calculate the determinants of the coefficient matrix and matrices obtained by replacing each column with the constants from the right-hand side, one at a time.**Determine Variable Values:**Use Cramer’s Rule to find the values of each variable by dividing the determinants obtained in step 3 by the determinant of the coefficient matrix.

By applying Cramer’s Rule, students can efficiently solve systems of linear equations and determine unique solutions for each variable in the system. This rule provides a structured method for handling simultaneous equations and is a valuable tool in the study of linear algebra.

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