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if A=[(1,2,3),(2,1,-1),(a,2,b)] is a mat...

if `A=[(1,2,3),(2,1,-1),(a,2,b)]` is a matrix satisfying `A A'=9I_(3,)` find the value of `|a|+|b|.`

Text Solution

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`rArr [(1,2,2),(2,1,-2),(a,2,b)][(1,2,a),(2,1,2),(2,-2,b)][(1,0,0),(0,1,0),(0,0,1)]`
`rArr [(9,0,a+2b+4),(0,9,2a-2b+2),(a+2b+4,2a-2b+2,a^(2)+b^(2)+4)]=[(9,0,0),(0,9,0),(0,0,9)]`
Equating the corresponding elements , we get
`a+2b+4=0`
`2a-2b+2=0`
and `a^(2)+b^(2)+4=9`
From Eqs. (i) and (ii),we get
a=-2 and b=-1
Hence,`|a|+|b|=|-2|+|-1|=2+1=3`
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