Question

Find $x$ if:$\left|\begin{array}{ccc}2& 1& x+1\\ -1& 3& -4\\ 0& -5& 3\end{array}\right|$ $=1$

Answer 1

$\left|\begin{array}{ccc}2& 1& x+1\\ -1& 3& -4\\ 0& -5& 3\end{array}\right|=1$

$\Rightarrow 2[3\times 3-(-4\left)\right(-5\left)\right]-1\left[\right(-1\left)\right(3)-(0\left)\right(-4\left)\right]+(x+1)\left[\right(-1\left)\right(-1)-(0\left)3\right]$

$\Rightarrow 2[9-20]-1\left[3\right]+(x+1)\left[5\right]=1$

$\Rightarrow -22+3+(x+1)\left(5\right)=1$

$\Rightarrow -19+(x+1)\left(5\right)=1$

$\Rightarrow (x+1)\left(5\right)=20$

$\Rightarrow (x+1)=4$

$\Rightarrow x=3$