find the value of cofficent μ in the following system from the determinat: 2x_1 +μx_2 +x_3 =0 (μ−1)x_1 −x_2 +2x_3 =0 4x


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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

	$[\begin{matrix} 2 & μ & 1 \\ μ - 1 & - 1 & 2 \\ 4 & 1 & 4 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}] = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}]$ $d e t : 2 (- 4 - 2) - μ [4 (μ - 1) - 8] + [(μ - 1) + 4] = 0$ $- 12 - 4 μ^{2} + 12 μ + μ + 3 = 0$ $- 4 μ^{2} + 13 μ - 9 = 0$ $μ = \frac{- 13 \pm \sqrt{169 - 144}}{- 8} = \frac{- 13 \pm 5}{- 8} = 1, \frac{9}{4}$
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