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Question
Mathematics
Let [ A ]3 × 3 be a non-singular matrix such that A -1=(1/3)( A 2-5 A +7 I ) Then 17 A 8-85 A 7+119 A 6-51 A 5-19 A 4+95 A 3-113 A 2+58 A + I =
Q. Let
[
A
]
3
×
3
be a non-singular matrix such that
A
−
1
=
3
1
(
A
2
−
5
A
+
7
I
)
Then
17
A
8
−
85
A
7
+
119
A
6
−
51
A
5
−
19
A
4
+
95
A
3
−
113
A
2
+
58
A
+
I
=
1567
258
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A
0
B
A
C
A
+
I
D
A
2
+
A
+
I
Solution:
For a non-singular matrix
A
3
×
3
, it is given that
A
−
1
=
3
1
(
A
2
−
5
A
+
7
I
)
⇒
A
3
−
5
A
2
+
7
A
−
3
I
=
0
…
(i)
17
x
5
−
19
x
∴
17
A
8
−
85
A
7
+
119
A
6
−
51
A
5
−
19
A
4
−
133
A
2
+
58
A
+
I
=
(
A
3
−
5
A
2
+
7
A
−
3
I
)
(
17
A
5
−
19
A
)
+
A
+
I
=
A
+
I
{
∵
A
3
−
5
A
2
+
7
A
−
3
I
=
0
}
