Question: Let A be an m x n matrix whose columns are linearly independent. a. Use Exercise 27 to show that A T A is an

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

a. Use Exercise 27 to show that ATA 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 ATA x = 0. This will show that Nul A = Nul ATA.

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