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e_1:\amp a_{11}x_{1}\amp +\amp a_{12}x_{2}\amp +\cdots+\amp a_{1n}x_{n}\amp =\amp b_1\\
e_2: \amp a_{21}x_{1}\amp +\amp a_{22}x_{2}\amp +\cdots+\amp a_{2n}x_{n}\amp =\amp b_2\\
\amp \vdots\amp \amp \vdots \amp \amp \vdots \amp \\
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a_{21}x_{1}\amp +\amp a_{22}x_{2}\amp +\cdots+\amp a_{2n}x_{n}\amp =\amp 0\\
\amp \vdots\amp \amp \vdots \amp \amp \vdots \amp \\
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\vdots \amp \amp \vdots \amp \amp \vdots \amp =\amp \\
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#3_{21} \amp #3_{22} \amp \cdots \amp #3_{2#2} \\
\vdots \amp \vdots \amp \ddots \amp \vdots \\
#3_{#1 1} \amp #3_{#1 2} \amp \cdots \amp #3_{#1 #2}
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a_{11} \amp a_{12} \amp \cdots \amp a_{1n} \amp b_{1}\\
a_{21} \amp a_{22} \amp \cdots \amp a_{2n} \amp b_{2}\\
\vdots \amp \vdots \amp \ddots \amp \vdots \amp \vdots\\
a_{m1} \amp a_{m2} \amp \cdots \amp a_{mn}\amp b_{m}
\end{amatrix}
}
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#3_{21} \amp #3_{22} \amp \cdots \amp #3_{2#2} \amp #4_{2}\\
\vdots \amp \vdots \amp \ddots \amp \vdots \amp \vdots\\
#3_{#1 1} \amp #3_{#1 2} \amp \cdots \amp #3_{#1 #2}\amp #4_{#1}
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\amp \vdots \\
#1_{#3,1} \amp #1_{#3,2} \amp \ldots \amp #1_{#3,#2}
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