Can You Use the Appended Matrix Method for 4x4 Determinants?

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SUMMARY

The discussion centers on the feasibility of using the appended matrix method for calculating the determinant of 4x4 matrices. It concludes that this method is ineffective for matrices larger than 3x3 due to the discrepancy in the expected number of terms, which should be n! (24 for 4x4) but results in only 8 terms. The row reduction method is identified as the most reliable technique for larger matrices, while expansion by minors is noted as a simpler alternative under certain conditions.

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  • Familiarity with matrix theory, particularly the properties of 4x4 matrices.
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Kevin McHugh
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I know row reduction methods are the best way to calculate the determinant of large matrices. I was wondering if you can use the appended matrix method to calculate the determinant of a 4x4 by appending the matrix with the first 3 columns. There should be n! terms, but I only get 8 instead of 24.
 
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I don't think the appended matrix method works for larger than 3x3 matrices for that reason.

The only other way I know for calculating the determinant is expansion by minors, which is n! terms, in principle, but it's a lot easier than it sounds if you have a lot of zeroes and ones.
 

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