Question

Evaluate the following 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