JEE Main 2020
Matrices & Determinants
Matrices and Determinants
Easy
Question
For which of the following ordered pairs (, ), the system of linear equations x + 2y + 3z = 1 3x + 4y + 5z = 4x + 4y + 4z = is inconsistent ?
Options
Solution
This problem asks us to identify for which ordered pair a given system of linear equations is inconsistent. We will use the conditions for consistency and inconsistency of a system of linear equations, often associated with Cramer's Rule or Gaussian elimination.
Key Concept: Conditions for Inconsistency of a System of Linear Equations
For a system of linear equations , where is the coefficient matrix and is the constant vector:
- Calculate the determinant of the coefficient matrix, .
- If , the system has a unique solution (consistent).
- If , the system either has infinitely many solutions (consistent) or no solution