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 already have discussed about Cramer’s rules, row equivalent matrix method in previous exercise of this chapter. In this exercise, we will go in deep about inverse matrix method. If you want the exercise of Cramer’s rules or equivalent matrix method then you can go to the previous exercise by clicking the button given below.

### Inverse Matrix Method in Class 12 Mathematics

The Inverse Matrix Method is a technique used to solve systems of linear equations by finding the inverse of the coefficient matrix. In Class 12 Mathematics, students learn about this method as a powerful tool for solving systems of linear equations efficiently.

## Matrix Based System of Linear Equations Notes PDF

This PDF will provide the solutions of every question from the 4th 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 the Inverse Matrix Method

The Inverse Matrix Method involves transforming the system of linear equations into matrix form and finding the inverse of the coefficient matrix. By multiplying the inverse of the coefficient matrix with the constant matrix, students can determine the values of the variables in the system of equations.

### Steps to Apply the Row Equivalent Matrix Method

**Formulate the System of Equations:**Write the given system of linear equations in standard form.**Construct Coefficient Matrix:**Create the coefficient matrix by arranging the coefficients of variables in a matrix format.**Find the Inverse Matrix:**Calculate the inverse of the coefficient matrix using appropriate methods, such as Gaussian elimination or adjoint method.**Determine Variable Values:**Multiply the inverse of the coefficient matrix with the constant matrix to obtain the values of the variables in the system of equations.

By utilizing the Inverse Matrix Method, students can efficiently solve systems of linear equations and determine unique solutions for each variable in the system. This method offers a systematic approach to solving simultaneous equations and is a valuable technique in linear algebra and matrix theory.

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