Paragraph: For the system of linear equations 2 x+3 y+5 z=9,7 x+3 y-2 z=8 and 2 x+3 y+λ z=μ Question: Under what condition does the above system of equations have unique solutions?

Correct answer: C. λ ≠ 5 and μ has any real value For unique solution : aligned & |A| ≠ 0 2(3 λ+6)-3(7 λ+4)+5(21-6) ≠ 0 & λ ≠ 5. aligned and μ can have any real value.

NDA 2016

Exam: NDA
Year: 2016
Subject: Mathematics
Chapter: Determinants

NDA 2016 · Mathematics · Determinants

Paragraph: For the system of linear equations 2 x+3 y+5 z=9,7 x+3...

Paragraph: For the system of linear equations

2 x+3 y+5 z=9,7 x+3 y-2 z=8

and

2 x+3 y+\lambda z=\mu

Question: Under what condition does the above system of equations have unique solutions?

Options

A $\lambda=5$ and $\mu=9$
B $\lambda \neq 9$ and $\mu=7$ only
C $\lambda \neq 5$ and $\mu$ has any real value
D $\lambda$ has any real value and $\mu \neq 9$

Correct answer

C. $\lambda \neq 5$ and $\mu$ has any real value

Step-by-step solution

For unique solution :

\begin{aligned} & |A| \neq 0 \Rightarrow 2(3 \lambda+6)-3(7 \lambda+4)+5(21-6) \neq 0 \\ & \Rightarrow \lambda \neq 5. \end{aligned}

and

\mu

can have any real value.$

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