Question

The following system of equation$3x - 2y + z = 0$,$\lambda x - 14y + 15z = 0$,$x + 2y - 3z = 0$has a solution other than $x = y = z = 0$for $\lambda$ equal to.

• A. 1
• B. 2
• C. 3
• D. 5

Answer 1

Answer: (D)

5

Answer 2

The system of equations has infinitely many (non-trivial) solution, if $\Delta = 0$ i.e., if $\left| \begin{matrix} 3 & - 2 & 1 \\ \lambda & - 14 & 15 \\ 1 & 2 & - 3 \end{matrix} \right| = 0$

⇒ $3(42 - 30) - \lambda(6 - 2) + 1( - 30 + 14) = 0$⇒ $\lambda = 5$.