91影视

If A is an matrix with row vectors $\stackrel{\mathbf{鈫�}}{{\mathbf{蝇}}_{\mathbf{1}}}\mathbf{,}\mathbf{.}\mathbf{.}\mathbf{.}\stackrel{\mathbf{鈫�}}{{\mathbf{蝇}}_{\mathbf{n}\mathbf{}}}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\stackrel{\mathbf{鈫�}}{\mathbf{x}}$ is a vector in ${\mathit{R}}^{\mathbf{m}}$ then,

$\mathit{A}\stackrel{\mathbf{鈫�}}{\mathbf{x}}\mathbf{=}\mathbf{\left[}\begin{array}{c}\mathbf{-}{\stackrel{\mathbf{鈫�}}{\mathbf{蝇}}}_{\mathbf{1}}\mathbf{-}\\ \mathbf{鈰�}\\ \mathbf{-}\stackrel{\mathbf{鈫�}}{{\mathbf{蝇}}_{\mathbf{n}}}\mathbf{-}\end{array}\mathbf{\right]}\stackrel{\mathbf{鈫�}}{\mathbf{x}}\mathbf{\left[}\begin{array}{c}\mathbf{-}{\stackrel{\mathbf{鈫�}}{\mathbf{蝇}}}_{\mathbf{1}}\mathbf{.}\stackrel{\mathbf{鈫�}}{\mathbf{x}}\mathbf{-}\\ \mathbf{鈰�}\\ \mathbf{-}\stackrel{\mathbf{鈫�}}{{\mathbf{蝇}}_{\mathbf{n}}}\mathbf{.}\stackrel{\mathbf{鈫�}}{\mathbf{x}}\mathbf{-}\end{array}\mathbf{\right]}$

The matrices are,

$A\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right],A\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right]$, and$A\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]=\left[\begin{array}{c}7\\ 8\\ 9\end{array}\right]$

The $3脳3$matrix A is,

role="math" localid="1664210907122" $A=\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$

Consider the matrices, $A\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

role="math" localid="1664211415683" $$\begin{gathered} \left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right] \\ \left[\begin{array}{c}a路鈥�1+b路鈥�0+c路鈥�0\\ d路鈥�1+e0+f路鈥�0\\ g路鈥�1+h路鈥�0+i路鈥�0\end{array}\right]=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right] \\ \left[\begin{array}{c}a\\ d\\ g\end{array}\right]=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right] \end{gathered}$$

Consider the matrices, $A\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right]$

$$\begin{gathered} \left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right] \\ \left[\begin{array}{c}a路鈥�0+b路鈥�1+c路鈥�0\\ d路鈥�0+e路1+f路鈥�0\\ g路鈥�0+h路鈥�1+i路鈥�0\end{array}\right]=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right] \\ \left[\begin{array}{c}b\\ e\\ h\end{array}\right]=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right] \end{gathered}$$

Consider the matrices,$A\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]=\left[\begin{array}{c}7\\ 8\\ 9\end{array}\right]$

role="math" localid="1664211626454" $$\begin{gathered} \left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right] \\ \left[\begin{array}{c}a路鈥�0+b路鈥�0+c路鈥�1\\ d路鈥�0+e路0+f路鈥�1\\ g路鈥�0+h路鈥�0+i路鈥�1\end{array}\right]=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right] \\ \left[\begin{array}{c}c\\ f\\ i\end{array}\right]=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right] \end{gathered}$$

Therefore, the values are, $\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]=\left[\begin{array}{ccc}1& 4& 7\\ 2& 5& 8\\ 3& 6& 9\end{array}\right]$.

Hence, a $3脳3$ matrix A such that $A\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right],A\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right]$and is $A\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]=\left[\begin{array}{c}7\\ 8\\ 9\end{array}\right]$.