Question bank/JEE Main/Mathematics
JEE MainMathematicsModerateMatrix and determinants
The system of linear equations
x+y+z=2
2 x+3y+2z=5
2x+3y+ (a^2 + 1)z = a+1
Show answer and solution
$D = \left| \begin{matrix}
1 & 1 & 1 \\
2 & 3 & 2 \\
2 & 3 & a^{2} - 1
\end{matrix} \right|$
$D = \left| \begin{matrix}
1 & 1 & 0 \\
2 & 1 & 0 \\
2 & 1 & a^{2} - 3
\end{matrix} \right| = a^{2} - 3$
Since if a^2≠3 then only it will have unique solution. So at a=4 unique
solution exist.
1 & 1 & 1 \\
2 & 3 & 2 \\
2 & 3 & a^{2} - 1
\end{matrix} \right|$
$D = \left| \begin{matrix}
1 & 1 & 0 \\
2 & 1 & 0 \\
2 & 1 & a^{2} - 3
\end{matrix} \right| = a^{2} - 3$
Since if a^2≠3 then only it will have unique solution. So at a=4 unique
solution exist.
Source: Grass-G / M-28 Mathematics Paper FST 16 Jan.docx
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