estion(14)
2 5
A =
C:
and A2 - 5A + 1 = 0 then a
b
A
1
Answers
Answered by
2
Answer:
We have, [
3
−1
1
2
]
∴A
2
=AA= [
3
−1
1
2
][
3
−1
1
2
]=[
8
−5
5
3
]
So, A
2
−5A+7I= [
8
−5
5
3
]−5[
3
−1
1
2
]+7[
1
0
0
1
]=[
8−15+7
−5+5+0
5−5+0
3−10+7
]=[
0
0
0
0
]=O
Now, A
2
−5A+7I=O
⇒A
−1
(A
2
−5A+7I)=A
−1
=O [Multiplying throughout by A
−1
]
⇒A
−1
A
2
−5A
−1
A+7A
−1
I=O
⇒A−5I+7A
−1
=O
⇒7A
−1
=5I−A
7A
−1
= [
5
0
0
5
]−[
3
−1
1
2
]=[
2
1
−1
3
]
⇒A
−1
=
7
1
[
2
1
−1
3
]
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