1.

Let A be a squarre matrix of order of order 3 satisfies the matrix equationA^(3)-6 A ^(2) + 7 A - 8 I = O and B = A- 2 I .Also, det A = 8.If adj((B/2)^(-1))= (p/q)B, where p,q in N , the least valuse of(p+q) is equal to

Answer»

<P>7
9
29
41

Solution :`becauseB = A -2I `
`therefore A^(-1) B = I - 2A^(-1)`...(i)
`adj[(B/2)^(-1)]= (B/2)/abs(B/2) = (B/2)/(1/8abs(B)) = (4B)/abs(B) = 4/10 B[becauseabs(B) = 10 ]`
`= 2/5 B = p/q B`[GIVEN]
`THEREFOREP= 2 and q = 5 `
Hence,p + q =7


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