Question:
If the following system of linear equations
$2 x+y+z=5$
$x-y+z=3$
$x+y+a z=b$
has no solution, then :
Correct Option: , 4
Solution:
Here $D=\left|\begin{array}{ccc}2 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & a\end{array}\right|=2(-a-1)-1(a-1)+1+1$
$D_{3}=\left|\begin{array}{ccc}2 & 1 & 5 \\ 1 & -1 & 3 \\ 1 & 1 & b\end{array}\right|=2(-b-3)-1(b-3)+5(1+1)$
for $a=\frac{1}{3}, b \neq \frac{7}{3}$, system has no solutions