Applications of Determinants:
Example: Find the area of a parallelogram whose sides are determined by vectors
(2,6) and (1,8).
Example: Find the volume of a parallelepiped whose sides are determined by
vectors (1,1,2), (0, 1,1) and (0, -1, 2).
Must know about linear transformations:
T(au+bv) = a T(u) + b T(v)
Example: If T(1,1) = (2,5) and T(2, 3)= (1,7), find T(5,6)=? Must know how to find the matrix representation of a linear transformation:
Example: T(x,y,z) = (x+y, x-z, x+2y-z).
Is T invertible?
Trace of T?