Correct Answer - Option 2 : it has only the trivial solution x = y = z = 0
3x + 2y + z = 0
x + 4y + z = 0
2x + y + uz = 0
Explanation:
Given system of equation can be written as
\(\left[ {\begin{array}{*{20}{c}} 3&2&1\\ 1&4&1\\ 2&1&4 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} x\\ y\\ z \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0\\ 0\\ 0 \end{array}} \right]\)
[i.e. [A] [x] = [B]
As per rules:
If |A| ≠ 0: trivial solution
If |A| = 0: non-trivial solution
\(\left| {\begin{array}{*{20}{c}} 3&2&1\\ 1&4&1\\ 2&1&4 \end{array}} \right| = 3\left( {16 - 1} \right) - 2\left( {4 - 2} \right) + 1\left( {1 - 8} \right)\)
= 45 – 4 – 7
≠ 0
∴ Solution is trivial solution
