Matrices and determinants mains 2018 solve please: Suppose A is any 3 X 3 non-singular matrix and (A-31)(A- 51) - Maths - Matrices

Question

M a t r i c e s   a n d   d e t e r m i n a n t s  
m a i n s   2018   s o l v e   p l e a s e :  
S u p p o s e   A   i s   a n y   3   X
  3   n o n - sin g u l a r     m a t r i x
  a n d   ( A - 31 ) ( A -   51 )   = O ,
  w h e r e     I = I 3   a n d   O = O 3
  I f     α A + ß A - 1 = 41 t h e n
  α + β   i s   e q u a l   t o
  : 1 8 2 13 3 12 4 7

Lovina Kansal · Accepted Answer

Dear student

Dear student
Consider,A-3IA-5I=O⇒A2-5AI-3IA+15I2=O⇒A2-5A-3A+15I=0⇒A2-8A=-15I⇒A-1A2-8A-1A=-15A-1I   Pre multiplying by A-1 on both sides⇒A-8I=-15A-1⇒A+15A-1=8I⇒12A+15AA-1=4IOn comparing with αA+βA-1=4I, we getα=12 and β=152So, α+β=12+152=8

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