Matrix Based System of Linear Equations Notes Class 12 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 already have discussed about Cramer’s rules in previous exercise of this chapter. In this exercise, we will go in deep about row equivalent matrix method. If you want the exercise of Cramer’s rules then you can go to the second exercise by clicking the button given below.

### Row Equivalent Matrix Method

One of the most fundamental techniques of solving a system like;

- a1x + b1y = c1
- a2x + b2y = c2

is the technique of elimination. We can illustrate this technique on the linear system.

## Matrix Based System of Linear Equations Notes Class 12 PDF

This PDF will provide the solutions of every question from the 3rd 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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### Row Equivalent Matrix Method in Class 12 Mathematics

The Row Equivalent Matrix Method is a technique used to solve systems of linear equations by transforming the system into an equivalent matrix form. In Class 12 Mathematics, students learn about this method as an alternative approach to solving systems of linear equations, particularly when dealing with larger systems or matrices.

### Understanding the Row Equivalent Matrix Method

The Row Equivalent Matrix Method involves performing a series of row operations on the augmented matrix of the system of linear equations to simplify and transform it into a row-echelon form or reduced row-echelon form. This process allows students to identify the solutions to the system of equations systematically.

### Steps to Apply the Row Equivalent Matrix Method

**Formulate the Augmented Matrix:**Write the system of linear equations in augmented matrix form, combining the coefficients of variables with the constants on the right-hand side.**Perform Row Operations:**Utilize row operations, such as interchange, scaling, and replacement, to manipulate the augmented matrix and transform it into row-echelon form or reduced row-echelon form.**Identify Solutions:**Analyze the row- echelon form or reduced row-echelon form of the matrix to determine the solutions of the system of linear equations. The solutions can be obtained directly from the final matrix representation.

By applying the Row Equivalent Matrix Method, students can effectively solve systems of linear equations by converting them into matrix form and using row operations to simplify the calculations. This method provides a structured and systematic approach to solving complex systems of linear equations and is a valuable tool in the study of linear algebra.

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