JEE Advanced 2023 Mathematics question
Let , and be real numbers. Consider the following system of linear equations
x + 2y + z = 7
x + α z = 11
2x - 3y + β z = γ
Match each entry in List-I to the correct entries in List-II. List-I (P) If and , then the system has (Q) If and , then the system has (R) If where and , then the system has (S) If where and , then the system has List-II (1) a unique solution (2) no solution (3) infinitely many solutions (4) , and as a solution (5) , and as a solution The correct option is:
Answer: (A)
Solution
, which is zero iff . Then the third row of coefficients equals , and the same combination of right sides gives . (P) , :
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