WBJEE · Maths · Determinants
The linear system of equations
\(\left.\begin{array}{l}8 x-3 y-5 z=0 \\ 5 x-8 y+3 z=0 \\ 3 x+5 y-8 z=0\end{array}\right\}\) has
- A only zero solution
- B only finite number of non-zero solutions
- C no non-zero solution
- D infinitely many non-zero solutions
Answer & Solution
Correct Answer
(D) infinitely many non-zero solutions
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} & 8x-3 y-5 z=0 \\ & 5 x-8 y+3 z=0 \\ & 3 x+5 y-8 z=0 \\ &D=\left|\begin{array}{ccc} 8 & -3 & -5 \\ 5 & -8 & 3 \\ 3 & 5 & -8 \end{array}\right| \\ &=8(64-15)+3(-40-9)-5(25+24) \\ =& 8 \times 49+3 \times(-49)-5 \times 49 \\ =& 0 \end{aligned} \]…
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