समीकरण [ * 20 c 1&0&1 - 1 &1&0 0& - 1 &1 ] , [ l x ] = [ l 1 1 2 ] का हल है, (x,y,z)=

माना A = [ * 20 c 1&0&1 - 1 &1&0 0& - 1 &1 ] , , A^ - 1 [ * 20 c 1 2 & - 1 2 & - 1 1 2 & 1 2 & - 1 2 1 2 & 1 2 & 1 2 ] AX = B X = A^ - 1 B , [ * 20 c 1 2 & - 1 2 & - 1 1 2 & 1 2 & - 1 2 1 2 & 1 2 & 1 2 ] , [ l 1 1 2 ] = [ l - 1 0 2 ]. वैकल्पिक : [ * 20 c 1&0&1 - 1 &1&0 0& - 1 &1 ] , , , , [ l x ] = [ l 1 1 2 ] [ l x + 0y + z - x + y + 0z 0x - y + z ] = [ l 1 1 2 ] x + z = 1 - x + y = 1 z - y = 2 (x, y, z) = ( - 1, 0, 2).

समीकरण [ * 20 c 1&0&1 - 1 &1&0 0& - 1 &1 ] , [ l x ] = [ l 1 1 2 …

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समीकरण $\left[ {\begin{array}{*{20}{c}}1&0&1\\{ - 1}&1&0\\0&{ - 1}&1\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ \begin{array}{l}1\\1\\2\end{array} \right]$ का हल है, $(x,y,z)$=

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माना $A = \left[ {\begin{array}{*{20}{c}}1&0&1\\{ - 1}&1&0\\0&{ - 1}&1\end{array}} \right]\, $
$\Rightarrow \,{A^{ - 1}}\left[ {\begin{array}{*{20}{c}}{\frac{1}{2}}&{\frac{{ - 1}}{2}}&{ - 1}\\{\frac{1}{2}}&{\frac{1}{2}}&{\frac{{ - 1}}{2}}\\{\frac{1}{2}}&{\frac{1}{2}}&{\frac{1}{2}}\end{array}} \right]$
$\therefore AX = B \Rightarrow X = {A^{ - 1}}B\,\left[ {\begin{array}{*{20}{c}}{\frac{1}{2}}&{\frac{{ - 1}}{2}}&{ - 1}\\{\frac{1}{2}}&{\frac{1}{2}}&{\frac{{ - 1}}{2}}\\{\frac{1}{2}}&{\frac{1}{2}}&{\frac{1}{2}}\end{array}} \right]$
$,\left[ \begin{array}{l}1\\1\\2\end{array} \right] = \left[ \begin{array}{l} - 1\\{\rm{ }}0\\{\rm{ }}2\end{array} \right]$.
वैकल्पिक : $\left[ {\begin{array}{*{20}{c}}1&0&1\\{ - 1}&1&0\\0&{ - 1}&1\end{array}} \right]\,\,\,\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ \begin{array}{l}1\\1\\2\end{array} \right]$
$ \Rightarrow \left[ \begin{array}{l}x + 0y + z\\ - x + y + 0z\\0x - y + z\end{array} \right] = \left[ \begin{array}{l}1\\1\\2\end{array} \right]$
$\Rightarrow x + z = 1$
$- x + y = 1$
$z - y = 2$
$ \Rightarrow (x, y, z) = ( - 1, 0, 2)$.

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