A 2 2 matrix B is upper triangular if [B]21 = 0. Let UT2 be the

Question:

A 2 × 2 matrix B is upper triangular if [B]21 = 0. Let UT2 be the set of all 2 × 2 upper triangular matrices. Then UT2 is a subspace of the vector space of all 2 × 2 matrices, M22 (you may assume this). Determine the dimension of UT2 providing all of the necessary justifications for your answer.