Question

Evaluate`Delta=|1a b c1b c a1c a b|`

Answer 1

`Delta = |[1,1,bc],[1,b,ca],[1,c,ab]|`
Applying `R_2->R_2-R_1` and `R_3->R_3-R_1`
`Delta = |[1,1,bc],[0,b-a,ca-bc],[0,c-a,ab-bc]|`
`Delta = (b-a)(c-a)|[1,1,bc],[0,1,-c],[0,1,-b]|`
Applying `R_3->R_3-R_2`
`Delta = (b-a)(c-a)|[1,1,bc],[0,1,-c],[0,0,c-b]|`
`Delta = (b-a)(c-a)[1(c-b)-0+0]`
`Delta = (b-a)(c-a)(c-b)`
`Delta = (a-b)(b-c)(c-a)`