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Evaluate the determinant of : If A = ...

Evaluate the determinant of :
If `A = |{:(1,1,-2),(2,1,-3),(5,4,-9):}|`, find |A|.

Text Solution

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`|A|=|{:(1,1,-2),(2,1,-3),(5,4,-9):}|`
`rArr" "|A|=|{:(1,1,-2),(2,1,-3),(5,4,-9):}|`
`=1|{:(1,-3),(4,-9):}|-1|{:(2,-3),(5,-9):}|+(-2)|{:(2,1),(5,4):}|`
(Expanding along`R_(2)`)
=1(-9+12)-1(-18+15)-2(8-5)
=3+3-6=0
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