Linear Transformations

Question 1

What is (A*B)^T?

Answer 1

B^T*A^T

Question 2

When can C = A*B?

Answer 2

When A is mn and B is np, then C is m*p.

Question 3

What does A*x = b mean?

Answer 3

That vector b is the mapping of vector x through the linear transformation defined by matrix A.

Question 4

What can be said about the columns of A?

Answer 4

That they are the mappings of the vectors of the basis.

e.g. if A = (2, 3; -1, 7) then A(1, 0) = (2 3) and A(0, 1) = (-1 7).