The system of equation 2 x+y-3 z=5 3 x-2 y+2 z=5 and 5 x-3 y-z=16

Correct answer: (B) is consistent, with a unique solution. Since | 2 1 -3 3 -2 2 5 -3 -1 |=26 ≠ 0 ⇒ System is consistent with unique solution.

Q171 / 270 · NDA 2018 (Phase 2) · Mathematics

The system of equation $\begin{aligned} & 2 x+y-3 z=5 \\ & 3 x-2 y+2 z=5 \text { and } \\ & 5 x-3 y-z=16 \end{aligned}$

A
is inconsistent
Correct answer
B
is consistent, with a unique solution
C
is consistent, with infinitely many solutions
D
has its solution lying along x -axis in three - dimensional space

Solution

Since $\left|\begin{array}{ccc}2 & 1 & -3 \\ 3 & -2 & 2 \\ 5 & -3 & -1\end{array}\right|=26 \neq 0$ $\Rightarrow$ System is consistent with unique solution.

Hence, the correct answer is option: 'B'.

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