Question

The system of linear equations x + y + z = 2 , 2x + 3y + 2z = 5     ,  2x + 3y + (a² – 1)z = a + 1

• (1)  is inconsistent when a = 4
• (2)  has infinitely many solutions for a = 4
• (3)  has a unique solution for | a| = √3 
• (4) is inconsistent when |a| = √3

Answer 1

Correct option is inconsistent when |a|=\(\sqrt3\) 

Solution::

\(D={\begin{vmatrix} 1&1&1\\2&3&2\\ 2 &3 &a^2-1 \end{vmatrix}}\) 

D=\(1(3a^2-3-6) - 1(2a^2-2-4) + 1(6-6)\) 

D=\(3a^2-9-2a^2+6\) 

D=\(a^2-3\)

\(\therefore |a|=\sqrt3\)

inconsistent when |a|=\(\sqrt3\)