Question

If the system of equations
$ax+y+2z=0x+2y+z=b2x+y+az=0$
has no solution, then $(a+b)$ can be equal to

• A. $-1$
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B), (C), (D)

The correct options are
B 2
C 3
D 4

$D=\left|\begin{array}{ccc}a& 1& 2\\ 1& 2& 1\\ 2& 1& a\end{array}\right|=0\Rightarrow a^2-a-2=0\Rightarrow (a-2)(a+1)=0\Rightarrow a=2\text{or}-1D_1=\left|\begin{array}{ccc}0& 1& 2\\ b& 2& 1\\ 0& 1& a\end{array}\right|;D_2=\left|\begin{array}{ccc}a& 0& 2\\ 1& b& 1\\ 2& 0& a\end{array}\right|;D_3=\left|\begin{array}{ccc}a& 1& 0\\ 1& 2& b\\ 2& 1& 0\end{array}\right|a=2\Rightarrow \text{infinite solution}a=-1,b\ne 0\text{has no solution}$
Hence, $(a+b)$ can be any value except $-1$