The system of linear equations

3x -2y -kz = 10

2x -4y -2z = 6

x + 2y -z = 5m

is inconsistent if

Option 1 -

^{$k \neq 3, m \neq \frac{4}{5}$}

Option 2 -

$k = 3, m \neq \frac{4}{5}$

Option 3 -

$k \neq 3, m \in R$

Option 4 -

k = 3, m = $\frac{4}{5}$

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Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

$Δ - | \begin{matrix} 3 & - 2 & - k \\ 2 & - 4 & - 2 \\ 1 & 2 & - 1 \end{matrix} | = | \begin{matrix} 3 & - 2 & - k \\ 0 & - 8 & 0 \\ 1 & 2 & - 1 \end{matrix} |, [R_{2} - R_{1} - 2 R_{3}]$

= 8 (3 + k)

For inconsistent $Δ = 0 \Rightarrow k = 3$

$Δ_{x} = | \begin{matrix} 10 & - 2 & - k \\ 6 & - 4 & - 2 \\ 5 m & 2 & - 1 \end{matrix} | = 32 - 40 m \neq 0 \Rightarrow m \neq \frac{4}{5}$

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The system of linear equations

3x -2y -kz = 10

2x -4y -2z = 6

x + 2y -z = 5m

is inconsistent if

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The system of linear equations 3x -2y -kz = 10 2x -4y -2z = 6 x + 2y -z = 5m is inconsistent if

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The system of linear equations

3x -2y -kz = 10

2x -4y -2z = 6

x + 2y -z = 5m

is inconsistent if