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Question Number 60303 by Cheyboy last updated on 19/May/19

Answered by tw000001 last updated on 18/Oct/19

$$\det \left|\begin{array}{ccc}2& -1& 5\\ 3& 4& 0\\ -2& 1& 9\end{array}\right|=154$$$$\to {\left[\begin{array}{ccc}2& -1& 5\\ 3& 4& 0\\ -2& 1& 9\end{array}\right]}^{-1}=\left[\begin{array}{ccc}\frac{18}{77}& \frac{1}{11}& -\frac{10}{77}\\ -\frac{27}{154}& \frac{2}{11}& \frac{15}{154}\\ \frac{1}{14}& 0& \frac{1}{14}\end{array}\right]$$$$\det \left|\begin{array}{ccc}9& 7& 5\\ 1& 4& 3\\ 7& 5& -2\end{array}\right|=-161$$$$\to {\left[\begin{array}{ccc}9& 7& 5\\ 1& 4& 3\\ 7& 5& -2\end{array}\right]}^{-1}=\left[\begin{array}{ccc}\frac{1}{7}& -\frac{39}{161}& -\frac{1}{161}\\ -\frac{1}{7}& \frac{53}{161}& \frac{22}{161}\\ \frac{1}{7}& -\frac{4}{161}& -\frac{29}{161}\end{array}\right]$$

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