Suppose \( A\in F^{n\times n} \)
\(
\exists!A^{-1}
\)
|
If suppose \( A\in F^{m\times n} \),rank(\( A \))=\( n\) \( Ax=0,\) \( x=O \text{ only }. \) |
Example: \( Ax=b \) \( A= \begin{bmatrix} 1 & 0 \\ 0 & 2 \\ 0 & 0 \end{bmatrix} , b= \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} , x= \begin{bmatrix} 0 \\ 0 \end{bmatrix} \) |