jee-main 2023 Q77

jee-main · India · session2_06apr_shift2 Matrices Linear System and Inverse Existence

For the system of equations $x + y + z = 6$ $x + 2y + \alpha z = 10$ $x + 3y + 5z = \beta$, which one of the following is NOT true?
(1) System has no solution for $\alpha = 3, \beta = 24$
(2) System has a unique solution for $\alpha = -3, \beta = 14$
(3) System has infinitely many solutions for $\alpha = 3, \beta = 14$
(4) System has a unique solution for $\alpha = 3, \beta = 14$

For the system of equations\\
$x + y + z = 6$\\
$x + 2y + \alpha z = 10$\\
$x + 3y + 5z = \beta$, which one of the following is NOT true?\\
(1) System has no solution for $\alpha = 3, \beta = 24$\\
(2) System has a unique solution for $\alpha = -3, \beta = 14$\\
(3) System has infinitely many solutions for $\alpha = 3, \beta = 14$\\
(4) System has a unique solution for $\alpha = 3, \beta = 14$

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