Consider a transformation $$T:R^{3} \rightarrow R^{2}$$ where $$R^{3}$$ and $$R^{2}$$ represent three and two dimensional real column vectors respectively. Also, T(x) = Ax for some matrix A and for each x in $$R^{3}$$ How many rows and colums does A have and what is its maximum possible rank?

A

Rows : 3; Columns: 2; Rank : 3

B

Rows: 3; Columns: 2; Rank: 2

C

Rows: 2; Columns: 3; Rank : 2

D

Rows: 2; Columns: 3; Rank: 3