求证明行列式方程a b b 1 p p^3b a b=(a+2b)(a-b)² 1 q q^3=(p-q)(q-r)(r-p)(p+q+r)b b a 1 r r^3
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![求证明行列式方程a b b 1 p p^3b a b=(a+2b)(a-b)² 1 q q^3=(p-q)(q-r)(r-p)(p+q+r)b b a 1 r r^3](/uploads/image/z/5442767-71-7.jpg?t=%E6%B1%82%E8%AF%81%E6%98%8E%E8%A1%8C%E5%88%97%E5%BC%8F%E6%96%B9%E7%A8%8Ba+b+b+1+p+p%5E3b+a+b%3D%EF%BC%88a%2B2b%EF%BC%89%EF%BC%88a-b%EF%BC%89%26%23178%3B+1+q+q%5E3%3D%28p-q%29%28q-r%29%28r-p%29%28p%2Bq%2Br%29b+b+a+1+r+r%5E3)
求证明行列式方程a b b 1 p p^3b a b=(a+2b)(a-b)² 1 q q^3=(p-q)(q-r)(r-p)(p+q+r)b b a 1 r r^3
求证明行列式方程
a b b 1 p p^3
b a b=(a+2b)(a-b)² 1 q q^3=(p-q)(q-r)(r-p)(p+q+r)
b b a 1 r r^3
求证明行列式方程a b b 1 p p^3b a b=(a+2b)(a-b)² 1 q q^3=(p-q)(q-r)(r-p)(p+q+r)b b a 1 r r^3
第一题:a b b b a b b a b
b a b=- a b b= b b a[两次行交换]
b b a b b a a b b
b a b b a b
= 0 (b-a) (a-b) = { 0 (b-a) (a-b) }÷b
0 (b-a)(b+a) b(b-a) 0 0 -(a-b)(a+2b)
=(a+2b)(a-b)² [对角线法则]
第二题:1 p p^3 1 p p^3
1 q q^3 = 0 (q-p) (q-p)(q^2+p^2+qp)
1 r r^3 0 (r-p) (r-p)(r^2+p^2+rp)
1 p p^3 1 p p^3
=0 (q-p) (q-p)(q^2+p^2+qp) = { 0 (q-p) (q-p)(q^2+p^2+qp) }÷(q-p)
0 0 (q-p)(r-p)(r^2-q^2+rp-qp) 0 0 (q-p)(r-p)(r-q)(r+q+p)
=(p-q)(q-r)(r-p)(p+q+r) [对角线法则]
由于是自己做的,仅供参考!
如果哪里不对也请指正!
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