Talk:Condition for Concurrency of Three Straight Lines

Linear Algebra Results

The result labeled with WIP is (part of) a standard result in linear algebra, yet I cannot find that result.

The only result, from a search, that links determinants with linear dependence is in Properties of Matrix Exponential#Nonvanishing Determinant, which states the result without proof.

I expect to find a series of equivalences concerning (real) non-singular/singular (square) matrices, with results on determinants, linear dependence, row, column and null spaces, ranks, solutions to systems of linear equations, etc..

I see bits and pieces like Simultaneous Linear Equations has Unique Solution iff Rank of Matrix of Coefficients equals Number of Columns, but no general page.

If there is no such page, I am prepared to create it with the help of Help:Equivalence Proofs. --RandomUndergrad (talk) 13:39, 11 March 2022 (UTC)

Yes, there are some appalling gaps in linear algebra. Sources worked through are either highly technical and abstract, like Warner, or ploddingly tedious, like some of the others I started processing. Finding the middle ground, in which a library of practical results are assembled, has not been done as well as for some other fields of mathematics.

Please feel free to join up the dots in whatever way you see fit. --prime mover (talk) 15:35, 11 March 2022 (UTC)