Suppose A is a 3×3 matrix and A = 1/3 $u_1\cdot uT_1$ + 1/4 $u_2\cdot uT_2$ + 2/5 $u_3\cdot uT_3$ with
$uT_1 = (0, 1, −1)$
$uT_2 = (1, 2, 2)$
$u_3 = (−2,1/2,1/2)$
Compute det(A).
I know how to find determinants of 3x3 matricies, but I'm confused how to start this one given this function. Do I just use the given transposes to find $u_1$, $u_2$ and $u_3$ and then use those as column vectors in the matrix?