Proving X is Full Column Rank Matrix if X^TX is Non-Singular

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Homework Statement


Show (in complete detail) that X is a full column rank matrix if and only if
X^TX is non-singular (invertible). Assume X is a real matrix.

X^T is X transpose

Homework Equations





The Attempt at a Solution

 
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What does the fact that X is of full rank imply about X? Secondly what does the fact that (X^TX) being invertible imply about what the previous statement concludes?
 


Show an attempt at solving the problem, please? Or at least say why you can't.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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