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

2个回答

  • 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!