What is the determinant of a column matrix? I figured it would not exist, or equal 0, knowing only the method for solving square matrices, but is there a different method for finding such a determinant?
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Determinant is defined only for square matrices. Determinant of a non-square matrix is not zero. It is just not defined.
Your problem can be thought of like finding square root of -9 or maybe arcsin(1.5) both of which are not defined (or do not exist).
So, the determinant of a column matrix is defined only when it is a 1x1 matrix, which equals the lone element.
frederick99
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@DanUznanski That's worse.$f\hspace{2 mm} \mathbb{R}^+\cup { 0} \to \mathbb{R}^+ \cup { 0} : f(x) = \sqrt{ x}$. – Nov 01 '16 at 17:25
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@frederick99, I think ' square root of -9 ' is not a proper example here. Example of arcsin(1.5) is enough. In my opinion removing the example of ' square root of -9 ' would make your answer better. – Md. Abu Nafee Ibna Zahid Feb 19 '18 at 05:28
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1they do exist depending on your base set... if you are working with complex numbers, they both exist... they do not exist in the real space... – Girardi Apr 14 '18 at 14:28