If the following system of linear equations

2x + y + z = 5

x – y + z = 3

x + y + az = b

has no solution, then:

Option 1 -

$a \neq - \frac{1}{3}, b = \frac{7}{3}$

Option 2 -

$a \neq \frac{1}{3}, b = \frac{7}{3}$

Option 3 -

$a = \frac{1}{3}, b \neq \frac{7}{3}$

Option 4 -

$a = - \frac{1}{3}, b \neq \frac{7}{3}$

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

2 months ago

Correct Option - 3

Detailed Solution:

$Δ = | \begin{matrix} 2 & 1 & 1 \\ 1 & - 1 & 1 \\ 1 & 1 & a \end{matrix} | = 2 (- a - 1) + (1 - a) + 2 = - 3 a + 1$

$Δ_{3} = | \begin{matrix} 2 & 1 & 5 \\ 1 & - 1 & 3 \\ 1 & 1 & b \end{matrix} | = 2 (- b - 1) + (3 - b) + 5 \times 2 = - 3 b + 7$

For a = $\frac{1}{3}, b \neq \frac{7}{3},$ $\frac{}{} \frac{}{}$ system has no solution

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If the following system of linear equations

2x + y + z = 5

x – y + z = 3

x + y + az = b

has no solution, then:

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If the following system of linear equations 2x + y + z = 5 x – y + z = 3 x + y + az = b has no solution, then:

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If the following system of linear equations

2x + y + z = 5

x – y + z = 3

x + y + az = b

has no solution, then: