In Exercise 3 of Section 2, some of the sets formed subspaces of . In each of these case...

In Exercise 3 of Section 2, some of the sets formed subspaces of . In each of these cases, find a basis for the subspace and determine its dimension.

Reference: Exercise 3:

Determine whether the following are subspaces of R^2×2:

(a) The set of all 2 × 2 diagonal matrices

(b) The set of all 2 × 2 triangular matrices

(c) The set of all 2 × 2 lower triangular matrices

(d) The set of all 2 × 2 matrices A such that a₁₂ = 1

(e) The set of all 2 × 2 matrices B such that b₁₁ = 0

(f) The set of all symmetric 2 × 2 matrices

(g) The set of all singular 2 × 2 matrices