给出一个方程组，有 $n$ 个未知数，$m$ 个方程：
$$a_{11}x_{1} + a_{12}x_{2} + ... + a_{1n}x_{n} = b_{1} \
a_{21}x_{1} + a_{22}x_{2} + ... + a_{2n}x_{n} = b_{2} \
... \
a_{m1}x_{1} + a_{m2}x_{2} + ... + a_{mn}x_{n} = b_{m}$$
考察增广矩阵，并按列分块：
$$A = egin{bmatrix}
a_{11} & a_{12} & ... & a_{1n} & b_{1} \
a_{21} & a_{22} & ... & a_{2n} & b_{2} \
... & ... & ... & ... & ...\
a_{m1} & a_{m2} & ... & a_{mn} & b_{m}
end{bmatrix} = egin{bmatrix}
alpha_{1} & alpha_{2} & ... & alpha_{n} & eta
end{bmatrix}$$
先给出结论：
$r(A) = r(A | b) = n$：方程组有唯一解
未完待续。。。。。。