Vedantu’s Chapter-8 System of Linear Equations Solutions - Free PDF Download for Class 12
FAQs on RS Aggarwal Class 12 Solutions Chapter-8 System of Linear Equations
1. How do the RS Aggarwal Class 12 Solutions for Chapter 8 help with board exam preparation?
The RS Aggarwal Class 12 Solutions for Chapter 8 provide detailed, step-by-step methods for solving systems of linear equations, which is a key topic in the CBSE 2025-26 syllabus. By practising these solutions, students learn the correct format for presenting answers in board exams, understand how to apply the matrix inversion method correctly, and build confidence in handling complex problems involving three variables.
2. What is the main method used to solve problems in RS Aggarwal Class 12 Chapter 8?
The primary method detailed in the solutions for this chapter is the matrix inversion method. A system of linear equations is first represented in the matrix form AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. The solution is then found using the formula X = A⁻¹B, which is applicable only if the determinant of matrix A is non-zero.
3. How can you determine if a system of linear equations is consistent or inconsistent using the methods from this chapter?
To check for consistency using the matrix form AX = B, you first calculate the determinant of A (det(A)).
If det(A) ≠ 0, the system is consistent and has a unique solution.
If det(A) = 0, you must then calculate (adj A)B.
If (adj A)B ≠ 0, the system is inconsistent and has no solution.
If (adj A)B = 0, the system could be either consistent (with infinitely many solutions) or inconsistent.
4. What is the significance of the determinant of the coefficient matrix being zero (det(A) = 0)?
When the determinant of the coefficient matrix A is zero, it signifies that the inverse of the matrix (A⁻¹) does not exist. Because the standard method relies on finding this inverse (X = A⁻¹B), its absence means a unique solution cannot be found. This condition points to two possibilities: the system either has no solution (inconsistent) or infinitely many solutions (consistent and dependent), which requires further investigation.
5. What types of questions are covered in the solutions for RS Aggarwal Chapter 8?
The solutions for Chapter 8 cover a variety of problems designed to build a thorough understanding of the topic. These include:
Solving systems of linear equations in two and three variables (e.g., finding x, y, and z).
Questions that specifically ask to check the consistency of a system.
Word problems that must first be translated into a system of linear equations before being solved using the matrix method.
6. Why is the matrix method considered a powerful technique for solving systems of linear equations?
The matrix method is powerful because it offers a systematic and organised approach that is less prone to calculation errors compared to algebraic methods like substitution or elimination, especially for systems with three or more variables. It provides a clear algorithm (find the determinant, find the adjoint, find the inverse, and solve) that can be applied consistently to any system with a unique solution.
7. What is the first step when solving a word problem using the methods from RS Aggarwal Chapter 8?
The crucial first step is to formulate the system of linear equations from the information given in the word problem. This involves identifying the unknown quantities, assigning variables to them (like x, y, z), and then translating the statements and conditions from the problem into mathematical equations. Once the equations are set up, you can convert them into the matrix form AX = B to solve.
