线性代数的行列式，求出上三角或下三角，谢谢 线性代数问题，如下图中的上，下三角行列式的答案是怎么得出来的...
\u7ebf\u6027\u4ee3\u6570\u7684\u884c\u5217\u5f0f\uff0c\u9898\u76ee\u505a\u4e0a\u4e09\u89d2\u6216\u4e0b\u4e09\u89d2\uff0c\u8981\u6b65\u9aa4\uff0c\u8c22\u8c22\uff01A =
2 1 4 1
4 1 2 3
3 4 1 2
2 3 4 1
r2-2r1, r3-r1, r4-r1
A =
2 1 4 1
0 -1 -6 1
1 3 -3 1
0 2 0 0
\u4ea4\u6362\u7b2c1,3\u884c
A = -
1 3 -3 1
0 -1 -6 1
2 1 4 1
0 2 0 0
r3-2r1
A = -
1 3 -3 1
0 -1 -6 1
0 -5 10 -1
0 2 0 0
r3-5r2, r4+2r2
A = -
1 3 -3 1
0 -1 -6 1
0 0 40 -6
0 0 -12 2
r3+3r4
A = -
1 3 -3 1
0 -1 -6 1
0 0 4 0
0 0 -12 2
r4+3r3
A = -
1 3 -3 1
0 -1 -6 1
0 0 4 0
0 0 0 2
= 1*1*4*2
= 8
\u5176\u5b9e\u5c31\u662f\u6309\u884c\u6309\u5217\u5c55\u5f00\uff0c\u5982\u56fe
|1 2 3 4 5|
|0 -5 -10 -15 -20|
|0 1 0 1 1|
|0 0 0 1 3|
|0 0 0 2 4|
D = -5*
|1 2 3 4 5|
|0 1 2 3 4|
|0 0 -2 -2 -3|
|0 0 0 1 3|
|0 0 0 0 -2|
D = -5*1*1(-2)*1*(-2) = -20
先把最后一行和第二行换了，行列式要加负号
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