Rozwiązać równanie
\(\displaystyle{ \left[\begin{array}{ccc}1&1&1\\2&-3&5\\-1&2&-1\end{array}\right]}\) \(\displaystyle{ \cdot}\) \(\displaystyle{ X}\)\(\displaystyle{ =\left[\begin{array}{ccc}4&\\-5&\\2&\end{array}\right]}\)
równanie macierz
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Gotta
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równanie macierz
\(\displaystyle{ \left[\begin{array}{ccc}1&1&1\\2&-3&5\\-1&2&-1\end{array}\right]}\) \(\displaystyle{ \cdot}\) \(\displaystyle{ X}\)\(\displaystyle{ =\left[\begin{array}{ccc}4&\\-5&\\2&\end{array}\right]}\)
A=\(\displaystyle{ \left[\begin{array}{ccc}1&1&1\\2&-3&5\\-1&2&-1\end{array}\right]}\)
det A=-9
\(\displaystyle{ A^{-1}=}\)\(\displaystyle{ \left[\begin{array}{ccc}-\frac{7}{9}&-\frac{3}{9}&\-\frac{8}{9}\\\frac{3}{9}&0&\frac{3}{9}\\-\frac{1}{9}&\frac{3}{9}&\frac{5}{9}\end{array}\right]}\)
\(\displaystyle{ \left[\begin{array}{ccc}-\frac{7}{9}&-\frac{3}{9}&-\frac{8}{9}\\\frac{3}{9}&0&\frac{3}{9}\\-\frac{1}{9}&\frac{3}{9}&\frac{5}{9}\end{array}\right]}\)\(\displaystyle{ \cdot}\)\(\displaystyle{ \left[\begin{array}{ccc}1&1&1\\2&-3&5\\-1&2&-1\end{array}\right]}\) \(\displaystyle{ \cdot}\) \(\displaystyle{ X}\)\(\displaystyle{ =}\)\(\displaystyle{ \left[\begin{array}{ccc}-\frac{7}{9}&-\frac{3}{9}&-\frac{8}{9}\\\frac{3}{9}&0&\frac{3}{9}\\-\frac{1}{9}&\frac{3}{9}&\frac{5}{9}\end{array}\right]\cdot}\)\(\displaystyle{ \left[\begin{array}{ccc}4&\\-5&\\2&\end{array}\right]}\)
\(\displaystyle{ X=}\)\(\displaystyle{ =\left[\begin{array}{ccc}3&\\3&\\-1&\end{array}\right]}\)
A=\(\displaystyle{ \left[\begin{array}{ccc}1&1&1\\2&-3&5\\-1&2&-1\end{array}\right]}\)
det A=-9
\(\displaystyle{ A^{-1}=}\)\(\displaystyle{ \left[\begin{array}{ccc}-\frac{7}{9}&-\frac{3}{9}&\-\frac{8}{9}\\\frac{3}{9}&0&\frac{3}{9}\\-\frac{1}{9}&\frac{3}{9}&\frac{5}{9}\end{array}\right]}\)
\(\displaystyle{ \left[\begin{array}{ccc}-\frac{7}{9}&-\frac{3}{9}&-\frac{8}{9}\\\frac{3}{9}&0&\frac{3}{9}\\-\frac{1}{9}&\frac{3}{9}&\frac{5}{9}\end{array}\right]}\)\(\displaystyle{ \cdot}\)\(\displaystyle{ \left[\begin{array}{ccc}1&1&1\\2&-3&5\\-1&2&-1\end{array}\right]}\) \(\displaystyle{ \cdot}\) \(\displaystyle{ X}\)\(\displaystyle{ =}\)\(\displaystyle{ \left[\begin{array}{ccc}-\frac{7}{9}&-\frac{3}{9}&-\frac{8}{9}\\\frac{3}{9}&0&\frac{3}{9}\\-\frac{1}{9}&\frac{3}{9}&\frac{5}{9}\end{array}\right]\cdot}\)\(\displaystyle{ \left[\begin{array}{ccc}4&\\-5&\\2&\end{array}\right]}\)
\(\displaystyle{ X=}\)\(\displaystyle{ =\left[\begin{array}{ccc}3&\\3&\\-1&\end{array}\right]}\)