Question

$$\begin{gathered} 46.ThematrixA=\left[\begin{array}{cc}-3& x\\ 4& 2/3\end{array}\right]doesnothaveaninverse.findthevalueofx. \\ A)-\frac{2}{3} \\ B)-\frac{1}{2} \\ C)0 \\ D)\frac{3}{4} \\ E)1 \end{gathered}$$

Answer 1

Dear student
$$\begin{gathered} \mathrm{For}\mathrm{the}\mathrm{matrix},\mathrm{A}=\left[\begin{array}{cc}-3& \mathrm{x}\\ 4& \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\end{array}\right] \\ \mathrm{does}\mathrm{not}\mathrm{have}\mathrm{an}\mathrm{inverse}. \\ \Rightarrow \left|\mathrm{A}\right|=0 \\ \Rightarrow \left|\begin{array}{cc}-3& \mathrm{x}\\ 4& \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\end{array}\right|=0 \\ \Rightarrow \left(\frac{2}{3}\times -3\right)-4\mathrm{x}=0 \\ \Rightarrow -2-4\mathrm{x}=0 \\ \Rightarrow 2+4\mathrm{x}=0 \\ \Rightarrow 4\mathrm{x}=-2 \\ \Rightarrow \boxed{\mathrm{x}=\frac{-1}{2}} \end{gathered}$$
Regards