Linear Algebra 13d: Elementary Matrix Exercises

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lem.ma/LA - Linear Algebra on Lemma
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[@MathTheBeautiful]

Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.

[@TuneCX]

One might be interested in "Finding the nth term of a quadratic sequence", for example #28. Solving system of equations result in formula for nth term (n^2+n)/2, 10th term is (100+10)/2=55

[@GordonYiu]

Thanks for sharing. May I know the software used here?

[@vineetmukim2365]

Sir, in exercise 22 (11:48), since the RHS is not an identity matrix (hence, row or column operation choice does matter) and the unknown matrix is being operated by an elementary matrix from LHS, shouldn't we consider row operations and not column? The answer does not change though.

[@celkat]

If I understand correctly, in Exercise 22 we're treating the unknown matrix as the elementary matrix that is right-multiplied to the given matrix (which happens to also be an elementary matrix), so we're looking for column operations that turn the given matrix into the resulting matrix on the RHS. (He also elaborates a few minutes later that Exercises 22 and 23 illustrate a pair of matrices that are not each other's inverses but that nonetheless commute)