Set of equations a + b - 2c = 0, 2a - 3b + c = 0 and a - 5b + 4c = α is consistent for α equal to

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3 and 4 .Determinants and Matrices

medium

Set of equations $a + b - 2c = 0,$ $2a - 3b + c = 0$ and $a - 5b + 4c = \alpha $ is consistent for $\alpha$ equal to

A

$1$

B

$0$

C

$-1$

D

$2$

Solution

(b) $a + b – 2c = 0$
$2a – 3b + c = 0$

$a – 5b + 4c = \alpha $

System is consistent, if $D = \left| {\,\begin{array}{*{20}{c}}1&1&{ – 2}\\2&{ – 3}&1\\1&{ – 5}&4\end{array}\,} \right|$=$0$

and ${D_1} = \left| {\,\begin{array}{*{20}{c}}0&1&{ – 2}\\0&{ – 3}&1\\\alpha &{ – 5}&4\end{array}\,} \right|$= 0 and ${D_2}$ also zero.

Hence, value of $\alpha $ is zero.

Standard 12

Mathematics

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