没有合适的资源?快使用搜索试试~ 我知道了~
首页同济大学线性代数答案详解
资源详情
资源评论
资源推荐

1˜Ù
SK1-1
1.
˜
A = (A, b)
Ù¥
A =
1 1 2 2
2 1 3 −1
1 −1 1 4
, b =
1
3
5
Ïdk
1 1 2 2
2 1 3 −1
1 −1 1 4
x
1
x
2
x
3
=
1
3
5
¤‚5•§|/ª
x
1
+ x
2
+ 2x
3
+ 2x
4
= 1,
2x
1
+ x
2
+ 3x
3
− x
4
= 3,
x
1
− x
2
+ x
3
+ 4x
4
= 5.
2.
1 2
a b
!
+
x y
3 4
!
=
3 −4
7 1
!
1 + x 2 + y
a + 3 b + 4
!
=
3 −4
7 1
!
1 + x = 3
2 + y = −4
a + 3 = 7
b + 4 = 1
¤±kx = 2, y = −6, a = 4, b = −3.
3.
1

(1)
A + 2B =
3 −1 2
2 1 −2
!
+ 2
1 5 1
−2 −1 0
!
=
3 + 2 −1 + 10 2 + 2
2 − 4 1 − 2 −2
!
=
5 9 4
−2 −1 −2
!
3A − B = 3
3 −1 2
2 1 −2
!
−
1 5 1
−2 −1 0
!
=
9 − 1 −3 − 5 6 − 1
6 + 2 3 + 1 −6
!
=
8 −8 5
8 4 −6
!
(2)
AB
T
=
3 −1 2
2 1 −2
!
1 −2
5 −1
1 0
=
3 − 5 + 2 −6 + 1
2 + 5 − 2 −4 − 1
!
=
0 −5
5 −5
!
A
T
B =
3 2
−1 1
2 −2
1 5 1
−2 −1 0
!
=
3 − 4 15 − 2 3
−1 − 2 −5 − 1 −1
2 + 4 10 + 2 2
=
−1 13 3
−3 −6 −1
6 12 2
2

4.
(A + B)(A − B) =
1 −3
1 2
!
+
2 0
3 −1
!!
1 −3
1 2
!
−
2 0
3 −1
!!
=
3 −3
4 1
!
−1 −3
−2 3
!
=
−3 + 6 −9 − 9
−4 − 2 −12 + 3
!
=
3 −18
−6 9
!
5.
A
2
+ 3A − 2B =
1 0 0
0 1 2
0 2 1
2
+ 3
1 0 0
0 1 2
0 2 1
− 2
1 0 0
0 2 5
0 5 2
=
1 0 0
0 5 4
0 4 5
+
3 0 0
0 3 6
0 6 3
+
−2 0 0
0 −4 −10
0 −10 −4
=
1 + 3 − 2 0 0
0 5 + 3 − 4 4 + 6 − 10
0 4 + 6 − 10 5 + 3 − 4
=
2 0 0
0 4 0
0 0 4
6. (1)
1
2
3
3 −2 1
=
3 −2 1
6 −4 2
9 −6 3
(2)
2 3 1
1
−1
2
= 2 − 3 + 2 = 1
3

(3)
x y z
1 1 −1
1 2 1
−1 1 0
x
y
z
=
x + y −z x + 2y + z −x + y
x
y
z
= (x
2
+ xy − xz) + (xy + 2y
2
+ yz) + (−xz + yz)
= x
2
+ 2y
2
+ 2xy − 2xz + 2yz
(4)
B =
0 1 0
0 0 1
0 0 0
K
A = I + B =
1 1 0
0 1 1
0 0 1
k > 2ž,B
k
= 0
A
n
= (I + B)
n
= I + nB +
n(n − 1)
2
B
2
+ 0
=
1 0 0
0 1 0
0 0 1
+
0 n 0
0 0 n
0 0 0
+
0 0
n(n−1)
2
0 0 0
0 0 0
=
1 n
n(n−1)
2
0 1 n
0 0 1
7. †AŒ†ÝB÷vAB = BA,
B =
a b
c d
!
4

=k
1 1
0 1
!
a b
c d
!
=
a b
c d
!
1 1
0 1
!
a + c b + d
c d
!
=
a a + b
c c + d
!
Ïd
a + c = a
b + d = a + b
c = c
d = c + d
⇒
(
c = 0
a = d
†AŒ†Ý•
B =
a b
0 a
!
,
Ù¥a, b•?¿ê.
8.
y²µ
(A
T
+ A)
T
= A + A
T
= A
T
+ A
(A
T
− A)
T
= A − A
T
= −(A
T
− A)
¤±A
T
+ A´é¡Ý,A
T
− A´‡é¡Ý.
9.
A
n
=
λ
1
λ
2
.
.
.
λ
n
n
=
λ
n
1
λ
n
2
.
.
.
λ
n
n
SK1-2
1.
A =
3 1
0 0
2 1 0 0
0 0 1 4
0 0 2 5
=
A
1
O
O A
2
!
5
剩余91页未读,继续阅读


















安全验证
文档复制为VIP权益,开通VIP直接复制

评论1