TS EAMCET · Maths · Determinants
The number of real values of ' \(a\) ', for which the system of equations \(2 x+3 y+a z=0\), \(x+a y-2 z=0\) and \(3 x+y+3 z=0\) has nontrivial solutions is
- A 2
- B 1
- C 0
- D Infinity
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
\( \det \begin{pmatrix} 2 & 3 & a \\ 1 & a & -2 \\ 3 & 1 & 3 \end{pmatrix} = 0 \) \( 2(3a - (-2)) - 3(3 - (-6)) + a(1 - 3a) = 0 \) \( 2(3a + 2) - 3(9) + a - 3a^2 = 0 \) \( 6a + 4 - 27 + a - 3a^2 = 0 \) \( -3a^2 + 7a - 23 = 0 \) \( 3a^2 - 7a + 23 = 0 \)…
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