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Suppose A is any 3*3 non singular matrix and (A-3I)(A-5I)=0. If xA+bA'=4I , then x+b= 8 7 13 12

Suppose A is any 3*3 non singular matrix and (A-3I)(A-5I)=0. If xA+bA'=4I , then x+b= 
 
8
 
7
 
13
 
12

Grade:

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
5 years ago
i think it should be A -1at the place of A’ in the question please let me know
Shrinithi sellam
14 Points
5 years ago

solve : (A - 3I)(A - 5I) = 0
A.A - 5AI - 3IA + 15I² = 0
A² - 5A - 3A + 15I = 0 [ as I² = I] 
A² - 8A + 15I = 0
A² - 8A = -15I 
A^-1 (A²) - A^-1(8A) = -A^-1 .15I 
A - 8I = -15A^-1 
A + 15A^-1 = 8I
1/2 A + 15/2 A^-1 = 4I 
compare this to aA +bA^-1 = 4I
we get, 
a =1/2 , b=15/2
so, 
a+b=8
hence, option (3) is correct.
 

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