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Question
If A=`[(1,0,1),(0,1,2),(0,0,4)]` then show that `|3A| = 27|A|`
Solution
`"A" = [(1,0,1),(0,1,2),(0,0,4)]`
`abs(3 "A") = abs ((3,0,3),(0,3,6),(0,0,12))`
L.H.S = |3A| = `|(3,0,3), (0,3,6), (0,0,12)|`
= `3|(3,6),(0,12)| - 0|(0,6), (0,12)| + 3|(0,3),(0,0)|`
= (3 × 36) - 0 + 3(0)
= 108
R.H.S = `27 |A| = 27 |(1,0,1), (0,1,2), (0,0,4)|`
= `27[1|(1,2),(0,4)| -0|(0,2), (0,4)| +1|(0,1),(0,0)|]`
= 27[1(4) - 0 + 0]
= 1082
Hence, |3A| = 27|A|
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