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Question
Let `A=[(1,-1,2),(0,2,-3),(3,-2,4)] and B = 1/3 [(-2,0,1),(9,2,-3),(6,1,λ)]`. If AB = I, then the value of λ is ______.
Options
`(-9)/4`
−2
`(-3)/2`
0
MCQ
Fill in the Blanks
Solution
Let `A=[(1,-1,2),(0,2,-3),(3,-2,4)] and B = 1/3 [(-2,0,1),(9,2,-3),(6,1,λ)]`. If AB = I, then the value of λ is −2.
Explanation:
Given
`A=[(1,-1,2),(0,2,-3),(3,-2,4)]`
`B=1/3[(-2,0,1),(9,2,-3),(6,1,λ)]`
Here, `AB=[(1,-1,2),(0,2,-3),(3,-2,4)]xx[(-2,0,1),(9,2,-3),(6,1,λ)]xx1/3`
`[(1,0,0),(0,1,0),(0,0,1)]=[(-2-9+12,0-2+2,1+3+2λ),(18 -18,0 + 4 - 3,0-6-3λ),(-6-18+24,0-4+4,3+6+4λ)]xx1/3`
`[(1,0,0),(0,1,0),(0,0,1)]= [(1,0,1+3+2λ),(0,1,-6-3λ),(0,0,3 + 6 +4λ)] xx1/3`
After equating `0 = (1+3+2λ)/3`
λ = −2
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