Originally Posted by

**aman_cc** Hi - Need help in understanding the following

Let

X be a n-dim vector space

Y be a m-dim vector space

A be a mxn matrix

Thus, AX defined a linear transformation,T from X into Y i.e. T: X -> Y

Image of X under T, T(X) is a subspace of Y

I need help in understanding and thus formally proving two concepts:

1. Rank of A (which say is defined as dim of row space or dim of col space) = dim of T(X)

2. Why is dim(row space of A) = dim(col space of A)

Any pointers would be welcome. Thanks