交大版线性代数第一章答案(18)

上海交通大学出版

法一： 当n 2时：

a1 b1a1 b2

a1 bn

a2 b1 an b1a2 b1 an b1b1a2 b1 an b1a2 b2 an b2

a2 bn an bn

a2 b2 an b2a2 b2 an b2b2

a1

a2 bn an bn

a2 bn an bn

bn

b1 b1

b1

a2 an

ab2 b2b2

a2 an

1

0 0 0

bn bnbn

a2 an

法二：

a1 b1a2 b1 an b1a110 011

1 1

a1 b2

a2 b2

an b2a210 0b1b2

b3 bn

0

a1 bn

a2 bn an bnan10 000

0

21，（1）加边

x1a1a2a3 an

1a2a3 ana1x2a0x1a2a3 an

3 ana1a2x0a1x2a3 anri r1 ri3 an

0a1a2x3 an(i 2,3, ,n)a1a2

a 3 xn

0a1a2a3 xnn

1a1a2a3 aain

1x a00 0i 1

xi ai

11

10x2 a2

0n

c0i 1

100x3 a3 0c1

i 1x c1

i a0i

0 1

x a nn

n

1 an

ixi i 1xi ai aii 1

（2）加边

a1a2x1 a1

00x2 a2

00 0

a3

0 x3 a3 0