For the system of linear equations: , consider the following statements : (A) The system has unique

Q: JEE Main 2022 Matrices & Determinants: For the system of linear equations: , consider the following statements : (A) The system has unique ...

The correct answer is A. This problem involves analyzing a system of linear equations to determine the nature of its solutions (unique, no solution, or infinite solutions) based on the parameter . We will use the powerful tool of determinants, specifically Cramer's Rule, to classify the system. **1. Key Concept: Cramer's Rule for Systems of Linear Equations** For a system of linear equations in three variables : We define the following determinants: * **

Question

For the system of linear equations: , consider the following statements : (A) The system has unique solution if . (B) The system has unique solution if k = 2 (C) The system has unique solution if k = 2 (D) The system has no solution if k = 2 (E) The system has infinite number of solutions if k 2. Which of the following statements are correct?

Accepted Answer

This problem involves analyzing a system of linear equations to determine the nature of its solutions (unique, no solution, or infinite solutions) based on the parameter $k$ . We will use the powerful tool of determinants, specifically Cramer's Rule, to classify the system.

1. Key Concept: Cramer's Rule for Systems of Linear Equations

For a system of linear equations in three variables $x, y, z$ : $a_1x + b_1y + c_1z = d_1$ $a_2x + b_2y + c_2z = d_2$ $a_3x + b_3y + c_3z = d_3$ We define the following determinants:

** $\Delta$

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(B) and (E) only

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(C) and (D) only

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(A) and (E) only

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(A) and (D) only

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