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

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(A) Let $A = \left[\begin{array}{ll}2 & -6 \ 1 & -2\end{array}ight]$.First,we find the determinant of $A$:$|A| = (2)(-2) - (-6)(1) = -4 + 6 = 2$.Si

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

Vedclass · Answer

(A) Let $A = \left[\begin{array}{ll}2 & -6 \ 1 & -2\end{array}ight]$.First,we find the determinant of $A$:$|A| = (2)(-2) - (-6)(1) = -4 + 6 = 2$.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 $\frac{1}{|A|} \left[\begin{array}{rr}d & -b \ -c & a\end{array}ight]$.Here,$a=2, b=-6, c=1, d=-2$.$A^{-1} = \frac{1}{2} \left[\begin{array}{rr}-2 & 6 \ -1 & 2\end{array}ight] = \left[\begin{array}{rr}-1 & 3 \ -\frac{1}{2} & 1\end{array}ight]$.

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ll}2 & -6 \\ 1 & -2\end{array}\right]$

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