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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
in All | 17 views

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|=$$\sqrt3$$

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