1.

Evaluate `|{:(265, 240, 219),(240, 225, 198), (219, 198, 181):}|`

Answer» Let the given determinant be `Delta`. Then,
`Delta =|{:(265, 240, 219),(240, 225, 198), (219, 198, 181):}|`
`=|{:(46, 21, 219),(42, 27, 198), (38, 17, 181):}|" "[C_(1) to (C_(1) -C_(3)) " and " C_(2) to (C_(2)-C_(3))]`
`=|{:(4, 21, " "9),(-12, 27, -72),(4, 17, " "11):}|" "[C_(1) to (C_(1) -2C_(2)) " and " C_(3) to (C_(3)-10C_(2))]`
`=|{:(0, 4, " "-2),(0, 78, -39),(4, 17, " "11):}|" "[R_(1) to (R_(1) -R_(3)) " and " R_(2) to (R_(2)+3R_(3))]`
`=2(39)|{:(0, 2, -1),(0, 2, -1),(4, 17, 11):}| " "["taking 2 common from "R_(1) " and 39 common from "R_(2)]`
`=(78 xx 0) =0 " "[because R_(1) " and"R_(2) " are identical"].`


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