Suppose V, W are finite dimensional vector spaces and T : V rightarrow W is injective. Show that dim (R (T)) = dim (V). (Show that if U1, . . . , ut is a basis of V then T (u1), . . . , T (ut) is a basis of R (T). )
Show transcribed image textSuppose V, W are finite dimensional vector spaces and T : V rightarrow W is injective. Show that dim (R (T)) = dim (V). (Show that if U1, . . . , ut is a basis of V then T (u1), . . . , T (ut) is a basis of R (T). )