find-the-value-of-cofficent-in-the-following-system-from-the-determinat-2x-1-x-2-x-3-0-1-x-1-x-2-2x-3-0-4x-1-x-2-4x-3-0-

Question Number 183240 by ali009 last updated on 23/Dec/22

f i n d t h e v a l u e o f c o f f i c e n t μ i n t h e f o l l o w i n g

s y s t e m f r o m t h e d e t e r m i n a t :

2 x_{1} + μ x_{2} + x_{3} = 0

(μ - 1) x_{1} - x_{2} + 2 x_{3} = 0

4 x_{1} + x^{2} + 4 x^{3} = 0

Answered by TheSupreme last updated on 24/Dec/22

[\begin{matrix} 2 & μ & 1 \\ μ - 1 & - 1 & 2 \\ 4 & 1 & 4 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}] = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}]

d e t : 2 (- 4 - 2) - μ [4 (μ - 1) - 8] + [(μ - 1) + 4] = 0

- 12 - 4 μ^{2} + 12 μ + μ + 3 = 0

- 4 μ^{2} + 13 μ - 9 = 0

μ = \frac{- 13 \pm \sqrt{169 - 144}}{- 8} = \frac{- 13 \pm 5}{- 8} = 1, \frac{9}{4}