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The system of linear equations $x + y + z = 2$, $2x + 3y + 2z = 5$, $2x + 3y + (a^2 - 1)z = a + 1$
(1) is inconsistent when $a = 4$
(2) has a unique solution for $|a| = \sqrt{3}$
(3) has infinitely many solutions for $a = 4$
(4) is inconsistent when $|a| = \sqrt{3}$
BETA
