Question 1

If A is an n x n matrix and the homogeneous system A^{T}x = 0 has a unique solution,

what can you say about the dimension of the row space and column space of A?

Question 2

Suppose A is an m x n matrix of rank r, and E is an n x m elementary matrix.

Let B = EA, indicate whether each statement is true or false.

(a) A and B have the same null space

(b) A and B have the same column space

(c) A and B have the same bases for row space