Матрично у-е

[PhilipMath]

AX+3E=B(на - 2 ра).
A=|1 2 3|
|1 4-4|
|2 6 8|

B=|1 2 3|
|0 4 5|
|1 6 7|
E-от 3-ти ред

[Реклама]

[nikko1]

[tex]AX+3E=B^2\Leftrightarrow AX=B^2-3E\Leftrightarrow X=A^{-1}(B^2-3E)=A^{-1}(\left(\begin{array}{rrr} 4& 28& 34\\ 5& 46& 55\\ 8& 68& 82\end{array}\right)-\left(\begin{array}{rrr} 3& 0& 0\\ 0& 3& 0\\ 0& 0& 3\end{array}\right))=A^{-1}\left(\begin{array}{rrr} 1& 28& 34\\ 5& 43& 55\\ 8& 68& 79\end{array}\right)=[/tex]
[tex]=\left(\begin{array}{rrr} {28\over 9}&{1\over 9}&{ -10\over 9} \\ -{8\over 9}&{ 1\over 9}& {7\over{18}} \\ -{1\over 9}& -{1\over 9}& {1\over 9}\end{array}\right)\left(\begin{array}{rrr} 1& 28& 34\\ 5& 43& 55\\ 8& 68& 79\end{array}\right)=\frac{1}{18}\left(\begin{array}{rrr} -94& 294& 434\\50& 114& 119\\4& -6& -20\end{array}\right).[/tex]

[Septerra]

май условието беше B^-2...

[nikko1]

[nikko1]

[tex]AX+3E=B^{-2}\Leftrightarrow AX=B^{-2}-3E\Leftrightarrow X=A^{-1}(B^{-2}-3E)[/tex]
[tex]B^{-1}=\frac{1}{4}\left(\begin{array}{rrr} 2& -48& 2\\ -5& -4& 5\\ 4& 4& -4\end{array}\right),\ B^{-2}=B^{-1}.B^{-1}=\frac{1}{4}\left(\begin{array}{rrr} 2& -48& 2\\ -5& -4& 5\\ 4& 4& -4\end{array}\right)\frac{1}{4}\left(\begin{array}{rrr} 2& -48& 2\\ -5& -4& 5\\ 4& 4& -4\end{array}\right)=\frac{1}{8}\left(\begin{array}{rrr} 16& 8& -12\\15&28&-25\\-14&-24& 22\end{array}\right).[/tex]

[tex]B^{-2}-3E=\frac{1}{8}\left(\begin{array}{rrr} -8& 8& -12\\15&4&-25\\-14&-24& -2\end{array}\right).[/tex]
[tex]A^{-1}=\frac{1}{9}\left(\begin{array}{rrr} 56& 2& -20\\-16& 2& 7\\-2& -2& 2\end{array}\right).[/tex]
[tex]X=\frac{1}{9}\left(\begin{array}{rrr} 56& 2& -20\\-16& 2& 7\\-2& -2& 2\end{array}\right)\frac{1}{8}\left(\begin{array}{rrr} -8& 8& -12\\15&4&-25\\-14&-24& -2\end{array}\right)=\frac{1}{72}\left(\begin{array}{rrr}-69& 468& -341\\30& -144& 64\\-21& -36& 35\end{array}\right).[/tex]