Looks like another great course is coming to the end! I really enjoyed my endeavors in such abstract material it really helped teach me how to think, as crazy as that sounds.

during our last week we were presented with some new interesting material we didn’t have much opportunity to explore such as Set countability, diagonalization, and Proof by induction which is a really powerful proof technique as i’ve seen it in my linear algebra textbook when the author proved many theorems such as proving the Determinant of the Identity maxtrix equals 1

I know this induction proof is valid because if you look closely the determinant of a triangular matrix is equal to the product of the diagonal entries of the matrix.

Here is the general proof structure using induction

I’m going to be exploring this proof technique much more next semester so stay tuned

check out my classmates blogs for another prospective on our experiences in this course http://nanalelfecsc165slog.wordpress.com/ and http://zanecsc165.blogspot.ca/

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Usually if they want to prove the properties of determinants, simple induction is the way to go. The determinant function is recursively defined and and it is easier to prove that a statement holds for a one-by-one matrix and (n + 1) by (n + 1) matrix if you assume an induction hypothesis.