TS EAMCET · Maths · Matrices
The positive value of 'a' for which the system of linear homogeneous equations \(x+a y+z=0, a x+2 y-z=0,2 x+3 y+z=0\) has non-trivial solutions is
- A \(0\)
- B \(1\)
- C \(\frac{1+\sqrt{5}}{2}\)
- D \(\frac{\sqrt{5}-1}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{1+\sqrt{5}}{2}\)
Step-by-step Solution
Detailed explanation
For non-trivial solutions, \(det(A) = 0\). \(\begin{vmatrix} 1 & a & 1 \\ a & 2 & -1 \\ 2 & 3 & 1 \end{vmatrix} = 0\) \(1(2 - (-3)) - a(a - (-2)) + 1(3a - 4) = 0\) \(1(5) - a(a+2) + (3a - 4) = 0\) \(5 - a^2 - 2a + 3a - 4 = 0\) \(-a^2 + a + 1 = 0\) \(a^2 - a - 1 = 0\)…
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