JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The system of linear equation \(x + y + z = 2, 2x + 3y + 2z = 5\), \(2x + 3y + (a^2 -1)\,z = a + 1\) then
- A is inconsistent when \(a = 4\)
- B has a unique solution for \(\left| a \right| = \sqrt 3 \)
- C has infinitely many solutions for \(a = 4\)
- D inconsistent when \(\left| a \right| = \sqrt 3 \)
Answer & Solution
Correct Answer
(D) inconsistent when \(\left| a \right| = \sqrt 3 \)
Step-by-step Solution
Detailed explanation
By applying Crammer's Rule \(D = \left| {\begin{array}{*{20}{c}} 1&1&1\\ 2&3&2\\ 2&3&{{a^2} - 1} \end{array}} \right|\) \( = 3\left( {{a^2} - 1} \right) - 6 - 2\left( {{a^2} - 1} \right) + 4\) \( = {a^2} - 1 - 2 = {a^2} - 3\) If…
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