Do non-square matrices have a determinant. If not, why?
No, they don't.. but I don't know why.
If it satisfies your curiousity, look into any linear algebra textbook and read the chapter on "Determinants." Assuming that you're still in high school, if you're not going to major in mathematics in college, then it really isn't that important.
we did not get a textbook with such information because matrices was simply an enrichment topic for the standard linear algebra curriculem.
Determinants are only defined for square matrices.
In the plane, the determinant of a linear transformation represents the scaling it does to areas of figures. Would it really make sense to talk about a scaling factor when you're going from areas to volumes (ie. changing dimensions)? This is what nonsquare matrices do.
You may also be interested in knowing that the NxN Determinant of the Coefficients of a Linear System of N equations in N unknowns can indicate whether this System has a SINGLE UNIQUE solution. If this Determinant is NON-ZERO, then the System has a SINGLE UNIQUE solution (although in some cases this solution may be all 0's). If the Determinant is ZERO (0), then the System either has a) NO solutions, or b) an INFINITE number of solutions. (In other words, for this latter "zero case", the System will never have one & only one single unique solution.) (Coefficients assumed Real.)
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