哈工大版线性代数与空间解析几何课后题答案(7)

2

2a 1ac2 ( 1)c1

b22b 1

c3 ( 1)c12

c2c 1

c4 ( 1)c12

d2d 1

4a 46a 94c 4

a2

2

2a 1262b 1262c 1262d 126x1

x12

2x22x32x4

4b 46b 9c3 ( 2)c2 b26c 9c4 ( 3)c3c

4d 46d 9d2

x13 c1x12 c2x1 c3

32

x2 c1x2 c2x2 c3

0

x1 a1

(3)

x12 b1x1 b2

2

x2 b1x2 b22x3 b1x3 b22x4 b1x4 b2

x13

3

x2

3x33x4

x2 a1x3 a1x4 a1

x2 32

x3 c1x3 c2x3 c3x3

x4

x12 b1x1

2

x2 b1x22x3 b1x32x4 b1x4

32x4 c1x4 c2x4 c3

c2 ( a1)c1 x1

x2

证：等式左端c ( b)c321

x3

c4 ( c3)c1

x4

c3 ( b1)c2x

2c4 ( c2)c2x3

x4

x1

x12

2x2

x13 c1x12 c2x1

32x2 c1x2 c2x232x3 c1x3 c2x332x4 c1x4 c2x4

x13 c1x12x cx

3

334

213214

x1x3x4

x12

2x2

x13

3x2

32c ( c)c c1x2x2x2413x

x

2

324

x

x cxx

2324

x

x

3334

等式右

端.

8．解关于未知数x的方程

x

(1) 3

1x 201x 20

26x 12

6 (x 1)x 1

x3

1x 2

0

0x

解：3

(x 1)[x(x 2) 3] (x 1)[x2 2x 3] (x 1)(x 3)(x 1) 0 所以x1 1,x2 3,x3 1.

a

(2) m

ax

xb

mm 0(m 0)

b

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