三元一次方程组：
[egin{cases}
x_1 + 3x_2 + x_3 = 2 \
3x_1 + 4x_2 + 2x_3 = 9 \
-x_1 - 5x_2 + 3x_3 = 10 \
2x_1 + 7x_2 + x_3 = 1
end{cases}
Longrightarrow
egin{pmatrix}
1 & 3 & 1 & 2 \
3 & 4 & 2 & 9 \
-1 & -5 & 4 & 10 \
2 & 7 & 1 & 1
end{pmatrix}
]
右式为一个(4)级矩阵
[(1)
egin{cases}
a_{11}x_1 + a_{12}x_2 + cdots + a_{1n}x_n = b_1 \
a_{21}x_1 + a_{22}x_2 + cdots + a_{2n}x_n = b_2 \
dots dots\
a_{s1}x_1 + a_{s2}x_2 + cdots + a_{sn}x_n = b_s
end{cases}
Longrightarrow
egin{pmatrix}
a_{11} & a_{12} & cdots & a_{1n} \
a_{21} & a_{22} & cdots & a_{2n} \
vdots & vdots & & vdots \
a_{s1} & a_{s2} & cdots & a_{sn}
end{pmatrix}
= A
]
[egin{pmatrix}
a_{11} & a_{12} & cdots & a_{1n} & b_1\
a_{21} & a_{22} & cdots & a_{2n} & b_2\
vdots & vdots & & vdots & vdots\
a_{s1} & a_{s2} & cdots & a_{sn} & b_s
end{pmatrix}
= Z
]
(A)为((1))的系数矩阵，(Z)为((1))的增广矩阵。