Question

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

Answer 1

Answer: (B)

0

Answer 2

$a + b - 2c = 0$

$2a - 3b + c = 0$

$a - 5b + 4c = \alpha$

System is consistent, if $D = \left| \begin{matrix} 1 & 1 & - 2 \\ 2 & - 3 & 1 \\ 1 & - 5 & 4 \end{matrix} \right|$= 0

and $D_{1} = \left| \begin{matrix} 0 & 1 & - 2 \\ 0 & - 3 & 1 \\ \alpha & - 5 & 4 \end{matrix} \right|$= 0 and $D_{2}$ also zero.

Hence, value of $\alpha$ is zero.