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

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(A) Let $A = \left[\begin{array}{ll}1 & 3 \ 2 & 7\end{array}ight]$.First,we find the determinant of $A$:$|A| = (1 	imes 7) - (3 	imes 2) = 7 - 6

Vedclass · Accepted Answer

$A^{-1}=\left[\begin{array}{cc}7 & -3 \ -2 & 1\end{array}ight]$

Vedclass · Answer

(A) Let $A = \left[\begin{array}{ll}1 & 3 \ 2 & 7\end{array}ight]$.First,we find the determinant of $A$:$|A| = (1 	imes 7) - (3 	imes 2) = 7 - 6 = 1$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.The formula for the inverse of a $2 	imes 2$ matrix $\left[\begin{array}{ll}a & b \ c & d\end{array}ight]$ is $\frac{1}{ad-bc} \left[\begin{array}{cc}d & -b \ -c & a\end{array}ight]$.Substituting the values $a=1, b=3, c=2, d=7$:$A^{-1} = \frac{1}{1} \left[\begin{array}{cc}7 & -3 \ -2 & 1\end{array}ight] = \left[\begin{array}{cc}7 & -3 \ -2 & 1\end{array}ight]$.

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ll}1 & 3 \\ 2 & 7\end{array}\right]$

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