Let λ ∈ R . The system of linear equations 2 x 1 - 4 x 2 + λ x 3 = 1 x 1 - 6 x 2 + x 3 = 2 λ x 1 - 10 x 2 + 4 x 3 = 3 is inconsistent for :

Question

Let &#955; &#8712; R . The system of linear equations 2 x 1 - 4 x 2 + &#955; x 3 = 1 x 1 - 6 x 2 + x 3 = 2 &#955; x 1 - 10 x 2 + 4 x 3 = 3 is inconsistent for :

Aicharya · Accepted Answer

Here, we will use Cramer's Rule according to which, $D = 0$ and, $D_{1} \neq 0$ if the system of linear equations is inconsistent. $D = |\begin{matrix} 2 & - 4 & λ \\ 1 & - 6 & 1 \\ λ & - 10 & 4 \end{matrix}| = 2 (- 24 + 10) + 4 (4 - λ) + λ (- 10 + 6 λ)$

$= 2 (3 λ^{2} - 7 λ - 6) = 2 (λ - 3) (3 λ + 2)$

$D = 0 \Rightarrow λ = 3, - \frac{2}{3}$

$D_{1} = |\begin{matrix} 1 & - 4 & λ \\ 2 & - 6 & 1 \\ 3 & - 10 & 4 \end{matrix}| = 1 (- 24 + 10) + 4 (8 - 3) + λ (- 20 + 18) = 2 (3 - λ)$

For $λ = - \frac{2}{3}, D_{1} \neq 0$

Let λ ∈ R . The system of linear equations 2 x 1 - 4 x 2 + λ x 3 = 1 x 1 - 6 x 2 + x 3 = 2…

Solution

Let &#955; &#8712; R . The system of linear equations 2 x 1 - 4 x 2 + &#955; x 3 = 1 x 1 - 6 x 2 + x 3 = 2…

Solution

Let λ ∈ R . The system of linear equations 2 x 1 - 4 x 2 + λ x 3 = 1 x 1 - 6 x 2 + x 3 = 2…