线性代数复习分析（线性方程组）_综合

3.1数字线性方程组
in this part , two question may be asked
1.find the exact solution
2.find the general solution
3.find the common solution
two basic way:Gaussian elimination and the crammer law
a mixed question

4.2带参数齐次方程组
the way
use the det to determine the existence of the solution

q u e s t i o n 1

$question 1$
description:please find the value of the a , which enables the matrix can have the nonverbal solution , and describe the general solution

? ? ? 8 3 a + 3 7 2 a + 2 1 3 a + 3 7 4 a ? ? ? (condition)

$\begin{pmatrix} 8 & 2 & 3a+3 \\ 3a+3 & a+2 & 7\\ 7 & 1 & 4a \end{pmatrix}\tag{condition}$
$s o l u t i o n$ $solution$
then the let the det == 0
then we can get that

? 4 a 2 ? 5 a + 9 = = 0 (1)

$-4a^2-5a+9==0\tag{1}$
then

a = = 1 o r a = = ? 9 4 (2)

$a== 1 or a == -\frac{9}{4}\tag{2}$ ;
in the former situlation
we can get

X = k (? 1 3, ? 5 3, 1) (solution 1)

$X=k(-\frac{1}{3},-\frac{5}{3},1)\tag{solution 1}$
in the latter
we can get that

X = k (19 8, ? 61 8, 1)

$X=k(\frac{19}{8},-\frac{61}{8},1)$
4.3数字非齐次方程组 4.4带参数非齐次方程组
the same way , deal with the augmented matrix not the coefficient matrix,or use the crammer law,also the questions ,but much more difficult and boring to calculate ，and please note the combination of different fields
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