ICSE Class X Math 2016 Solved Paper | Question 2

ICSE Class X Math 2016 Solved Paper

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Question : 2

Total: 57

Given A=[

2	0
−1	7

] and I=[

1	0
0	1

] and A2= 9A+mI. Find m.

Solution:

Given :
A=[

2	0
−1	7

] and I=[

1	0
0	1

]
‌A2=A⋅A=[

2	0
−1	7

][

2	0
−1	7

]
‌‌=[

4	0
−2−7	0+49

]
‌‌=[

4	0
−9	49

]
‌9A+mI=9[

2	0
−1	7

]+m[

1	0
0	1

]
=[

18	0
−9	63

]+[

m	0
0	m

]
‌‌=[

18+m	0
−9	63+m

]
Now, According to question,
A2‌=9A+mI
[

4	0
−9	49

]‌=[

18+m	0
−9	63+m

]
comparing both sides,
4‌=18+m‌ and ‌49=63+m
⇒ m‌=−14

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