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UPSC NDA II 2018 Mathematics Solved Paper

Question : 21 of 120

Marks: +1, -0

2x+y-3z=5

3x-2y+2z=5

5x-3y-z=16

Solution: 👈: Video Solution

Given: The system of equations

2x+y-3z=5

3x-2y+2z=5 \;\text{ and }\;

5x-3y-z=16

A=\begin{bmatrix} 2 & 1 & -3 \\ 3 & -2 & 2 \\ 5 & -3 & -1 \end{bmatrix}

\det(A)=|A|=2 \times\{(-2 \times -1)-(-3 \times 2)\}-1 \times\{(3 \times -1)-(2 \times 5)\}+(-3) \times\{(3 \times -3)-(5 \times -2)\}

\Rightarrow|A|=2 \times (2+6)-1 \times (-3-10)-3 \times (-9+10)

\Rightarrow|A|=16+13-3=26

\therefore |A| \neq 0

So, system is consistent having unique solution.

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