Let A be an m x n matrix whose columns are linearly independent.

a. Use Exercise 27 to show that A^TA is an invertible matrix.
b. Explain why A must have at least as many rows as columns.
c. Determine the rank of A.

Data From Exercise 27

Let A be an m x n matrix. Use the steps below to show that a vector x in Rⁿ satisfies A x = 0 if and only if A^TA x = 0. This will show that Nul A = Nul A^TA.