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Using Cofactors of elements of second row, evaluate `Delta=|5 3 8 2 0 1 1 2 3|`

Answer» `Delta=|{:(5,3,8),(2,0,1),(1,2,3):}|.`
Cofactors of the elements of second row
`A_(21)=(-1)^(2+1)|{:(3,8),(2,3):}|=-(9-16)=7`
`A_(22)=(-1)^(2+2)|{:(5,8),(1,3):}|=(15-8)=7`
`A_(23)=(-1)^(2+3)|{:(5,3),(1,2):}|=(10-3)=7`
`therefore" "Delta=a_(21)A_(21)+a_(22)A_(22)+a_(23)A_(23)`
`=2xx7+0xx7+xx(-7)`
=14+0-7=7


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