Question

Find the value of determinant :

`|("a", "h", "g"),("h", "b", "f"),("g", "f", "c")|`

Answer 1

`|("a", "h", "g"),("h", "b", "f"),("g", "f", "c")|`

= `"a"|("b", "f"),("f", "c")| - "h"|("h", "f"),("g", "c")| + "g"|("h","b"),("g", "f")|`

= a(bc – f²) – h(hc – gf) + g(hf – gb)

= abc – af² – h²c + fgh + fgh – g²b

= abc + 2fgh – af² – bg² – ch²