Solution
= Solution
The line/plane decomposition gives
$$
\det A=(\alpha+\beta)(\alpha^2+\gamma^2).
$$
Substituting the values in part (a) and simplifying yields
$$
\boxed{\det A=\frac12(a+b+c)\bigl((a-b)^2+(b-c)^2+(c-a)^2\bigr).}
$$
= Solution
The line/plane decomposition gives
$$
\det A=(\alpha+\beta)(\alpha^2+\gamma^2).
$$
Substituting the values in part (a) and simplifying yields
$$
\boxed{\det A=\frac12(a+b+c)\bigl((a-b)^2+(b-c)^2+(c-a)^2\bigr).}
$$