线性代数学习辅导_答案1
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2022-08-03
19:15:45
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z
E
1.
} b 1 2 = m
D =
1 2 1
2 3 a + 2
1 a −2
r
2
+ r
1
× (−2)
r
3
− r
1
1 2 1
0 −1 a
0 a −2 −3
= 3 −a(a − 2) = −a
2
+ 2a + 3 = −(a − 3)(a + 1)6= 0.
e
, a 6= 3
a 6= −1.
^ $
A =
1 2 1
2 3 a + 2
1 a −2
r
2
+r
1
×(−2)
−−−−−−→
r
3
−r
1
1 2 1
0 −1 a
0 a − 2 −3
r
3
+r
2
×(a−2)
−−−−−−−→
1 2 1
0 −1 a
0 0 −3 + a
2
− 2a
,
g ? u p h : +
r(A) = 3.
j J
a
2
− 2a − 3 = (a − 3)(a + 1)6= 0.
O
,a 6= 3
a 6= −1.
2.
}
(
^ $
)
˜
A =
1 2 1 1
2 3 a + 2 3
1 a −2 0
r
2
+r
1
×(−2)
−−−−−−→
r
3
−r
1
1 2 1 1
0 −1 a 1
0 a − 2 −3 −1
r
3
+r
2
×(a−2)
−−−−−−−→
1 2 1 1
0 −1 a 1
0 0 a
2
− 2a − 3 a − 3
,
r(A) 6= r(
˜
A)
F
,
? u W +
.
a
2
− 2a − 3 = (a − 3)(a + 1) 6= 0
F
,r(A) = r(
˜
A) = 3,
u h T b +
;
a = 3
F
,r(A) = r(
˜
A) = 2 < 3,
u h W A +
;
a = −1
F
,
˜
A →
1 2 1 1
0 −1 −1 1
0 0 0 −4
,
r(A) = 2 6= r(
˜
A) = 3,
u W +
.
O
,
Æ U
a = −1.
3.
}
(
^ $
)
? u h 7 S + \ 8
,
k # s uh W A +
.
˜
A=
1 −1 −a 3
2 0 −3 1
−2 a 10 4
r
3
+r
2
−−−−−−−→
r
2
+r
1
×(−2)
1 −1 −a 3
0 2 −3 + 2a −5
0 a 7 5
1
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