Mathematics, 10.12.2019 00:31 evryday2285
Find the inverse of the given matrix, if it exists. aequals=left bracket start 3 by 3 matrix 1st row 1st column 1 2nd column 0 3rd column negative 2 2nd row 1st column 4 2nd column 1 3rd column 3 3rd row 1st column negative 4 2nd column 2 3rd column 3 endmatrix right bracket 1 0 −2 4 1 3 −4 2 3
Answers: 3
![A^{-1}=\left[ \begin{array}{ccc} \frac{1}{9} & \frac{4}{27} & - \frac{2}{27} \\\\ \frac{8}{9} & \frac{5}{27} & \frac{11}{27} \\\\ - \frac{4}{9} & \frac{2}{27} & - \frac{1}{27} \end{array} \right]](/tpl/images/0410/7878/27714.png)
![A=\left[ \begin{array}{ccc} 1 & 0 & -2 \\\\ 4 & 1 & 3 \\\\ -4 & 2 & 3 \end{array} \right]](/tpl/images/0410/7878/045e8.png)
![\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 4&1&3&0&1&0 \\\\ -4&2&3&0&0&1\end{array}\right]](/tpl/images/0410/7878/37e0b.png)
![\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ -4&2&3&0&0&1\end{array}\right]](/tpl/images/0410/7878/ceac3.png)
![\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ 0&2&-5&4&0&1\end{array}\right]](/tpl/images/0410/7878/3da2a.png)
![\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ 0&0&-27&12&-2&1\end{array}\right]](/tpl/images/0410/7878/56925.png)
![\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ 0&0&1&- \frac{4}{9}&\frac{2}{27}&- \frac{1}{27}\end{array}\right]](/tpl/images/0410/7878/ebd0a.png)
![\left[ \begin{array}{ccc|ccc}1&0&0&\frac{1}{9}&\frac{4}{27}&- \frac{2}{27} \\\\ 0&1&11&-4&1&0 \\\\ 0&0&1&- \frac{4}{9}&\frac{2}{27}&- \frac{1}{27}\end{array}\right]](/tpl/images/0410/7878/33afd.png)
![\left[ \begin{array}{ccc|ccc}1&0&0&\frac{1}{9}&\frac{4}{27}&- \frac{2}{27} \\\\ 0&1&0&\frac{8}{9}&\frac{5}{27}&\frac{11}{27} \\\\ 0&0&1&- \frac{4}{9}&\frac{2}{27}&- \frac{1}{27}\end{array}\right]](/tpl/images/0410/7878/42beb.png)
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Find the inverse of the given matrix, if it exists. aequals=left bracket start 3 by 3 matrix 1st row...
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