Find the inverse of the matrix,if it exists: | vedclass

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(A) Let $A = \left[\begin{array}{ll}2 & 1 \ 1 & 1\end{array}ight]$.First,we find the determinant of $A$:$|A| = (2)(1) - (1)(1) = 2 - 1 = 1$.Since $

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$A^{-1}=\left[\begin{array}{cc}1 & -1 \ -1 & 2\end{array}ight]$

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(A) Let $A = \left[\begin{array}{ll}2 & 1 \ 1 & 1\end{array}ight]$.First,we find the determinant of $A$:$|A| = (2)(1) - (1)(1) = 2 - 1 = 1$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.The inverse of a $2 	imes 2$ matrix $\left[\begin{array}{ll}a & b \ c & d\end{array}ight]$ is given by $\frac{1}{|A|} \left[\begin{array}{cc}d & -b \ -c & a\end{array}ight]$.Substituting the values $a=2, b=1, c=1, d=1$:$A^{-1} = \frac{1}{1} \left[\begin{array}{cc}1 & -1 \ -1 & 2\end{array}ight] = \left[\begin{array}{cc}1 & -1 \ -1 & 2\end{array}ight]$.

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ll}2 & 1 \\ 1 & 1\end{array}\right]$

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