Aspire Faculty ID #18336 · Topic: AMU MCA 2017 · Just now
AMU MCA 2017

If the system of equations
$2x+ay+6z=8$
$x+2y+bz=5$
$x+y+3z=4$

has a unique solution then

Solution

Determinant $\ne 0$ $\left|\begin{matrix}2 & a & 6 \ 1 & 2 & b \ 1 & 1 & 3\end{matrix}\right| \ne 0$ $=2(6-b)-a(3-b)+6(1-2)$ $=12-2b-3a+ab-6$ $=ab-3a-2b+6$ $=(a-2)(3-b)\ne 0$ $\Rightarrow a\ne2$ or $b\ne3$
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