Question

If the system of equations $x+2y-3z=1,(p+2)z=3,(2p+1)y+z=2$ is inconsistent, then the value of $p$ is

• A. $-2$
• B. $\frac{-1}{2}$
• C. $0$
• D. $2$

Answer 1

The correct option is A $-2$

Augumented matrix is $\left[\begin{array}{cccc}1& 2& -3& 1\\ 0& 0& p+2& 3\\ 0& 2p+1& 1& 2\end{array}\right]$

interchanging $R_2$ and $R_3$ gives

$\left[\begin{array}{cccc}1& 2& -3& 1\\ 0& 2p+1& 1& 2\\ 0& 0& p+2& 3\end{array}\right]$

given system is inconsistent if $p+2=0$

$\therefore p=-2$

Hence, option A.