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The ordered pair (a, b), for which the system of linear equations

3x – 2y + z = b

5x – 8y + 9z = 3

2x + y + az = -1

has no solution, is:

Option 1 -

$(3, \frac{1}{3})$

Option 2 -

$(- 3, \frac{1}{3})$

Option 3 -

$(- 3, - \frac{1}{3})$

Option 4 -

$(3, - \frac{1}{3})$

3 Views | Posted 2 weeks ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

2 weeks ago

Correct Option - 2

Detailed Solution:

System of equation can be written as

$(\begin{matrix} 3 & - 2 & 1 \\ 5 & - 8 & 9 \\ 2 & 1 & a \end{matrix}) (\begin{array}{l} x \\ y \\ z \end{array}) = (\begin{array}{l} b \\ 3 \\ - 1 \end{array})$

$(\begin{matrix} 3 & - 2 & 1 \\ 15 & - 24 & 27 \\ 6 & 3 & 3 a \end{matrix}) (\begin{array}{l} x \\ y \\ z \end{array}) = (\begin{array}{l} b \\ 9 \\ - 3 \end{array})$

$R_{3} - 2 R_{1}, R_{2} - 5 R_{1}$

for no solution

3a + 9 = 0 but $\frac{3}{2} - \frac{9 b}{2} \neq 0$

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

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The ordered pair (a, b), for which the system of linear equations

3x – 2y + z = b

5x – 8y + 9z = 3

2x + y + az = -1

has no solution, is:

1 Answer

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The ordered pair (a, b), for which the system of linear equations 3x – 2y + z = b 5x – 8y + 9z = 3 2x + y + az = -1 has no solution, is:

1 Answer

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Your Question

The ordered pair (a, b), for which the system of linear equations

3x – 2y + z = b

5x – 8y + 9z = 3

2x + y + az = -1

has no solution, is: