线性代数(2)(3)两题,要清晰地具体过程,
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线性代数(2)(3)两题,要清晰地具体过程,
![](http://img.wesiedu.com/upload/f/92/f926c3ae3c4ed7ae368a6c02feaa3331.jpg)
题目要求是:计算下列行列式
![](http://img.wesiedu.com/upload/f/92/f926c3ae3c4ed7ae368a6c02feaa3331.jpg)
题目要求是:计算下列行列式
![线性代数(2)(3)两题,要清晰地具体过程,](/uploads/image/z/16094824-16-4.jpg?t=%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%882%EF%BC%89%EF%BC%883%EF%BC%89%E4%B8%A4%E9%A2%98%2C%E8%A6%81%E6%B8%85%E6%99%B0%E5%9C%B0%E5%85%B7%E4%BD%93%E8%BF%87%E7%A8%8B%2C)
-1 4 3 1
2 -2 -1 3
1 2 3 1
3 0 2 4
r1+2r2,r3+r2
3 0 1 7
2 -2 -1 3
3 0 2 4
3 0 2 4
= 0 (两行相等则行列式等于0)
a b a+b
b a+b a
a+b a b
c1+c2+c3
2a+2b b a+b
2a+2b a+b a
2a+2b a b
r2-r1,r3-r1
2a+2b b a+b
0 a -b
0 a-b -a
= (2a+2b)(-a^2-(b^2-ab))
= -2(a+b)(a^2-ab+b^2)
= -2(a^3+b^3)
2 -2 -1 3
1 2 3 1
3 0 2 4
r1+2r2,r3+r2
3 0 1 7
2 -2 -1 3
3 0 2 4
3 0 2 4
= 0 (两行相等则行列式等于0)
a b a+b
b a+b a
a+b a b
c1+c2+c3
2a+2b b a+b
2a+2b a+b a
2a+2b a b
r2-r1,r3-r1
2a+2b b a+b
0 a -b
0 a-b -a
= (2a+2b)(-a^2-(b^2-ab))
= -2(a+b)(a^2-ab+b^2)
= -2(a^3+b^3)