# The system of linear equaltions. x + y + z = 0, 2x + 3y + 2z = 5, 2x + 3y + (a^2 − 1)z = a + 1

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The system of linear equaltions.

$x+y+z=0$

$2x+3y+2z=5$

$2x+3y+(a^2-1)z=a+1$

(1) has infinitely many solutions for $a=4$

(2) is inconsistent when $|a|=\sqrt3$

(3) is inconsistent when $a=4$

(4) has a unique solution for $|a|=\sqrt3$
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Matrices and Determinants, Applications of matrices and determinants
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Solve by matrix method