{"type":"video","version":"1.0","html":"<iframe src=\"https://www.loom.com/embed/d24eda16e7694ad08f4a14e2d991b866\" frameborder=\"0\" width=\"1838\" height=\"1378\" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>","height":1378,"width":1838,"provider_name":"Loom","provider_url":"https://www.loom.com","thumbnail_height":1378,"thumbnail_width":1838,"thumbnail_url":"https://cdn.loom.com/sessions/thumbnails/d24eda16e7694ad08f4a14e2d991b866-0e0c77ab68d2edba.gif","duration":4485.123,"title":"9FM0 CP2 - Set 2 - Proof by Induction V2","description":"I walk through several induction style proofs, starting with matrix powers using a base case, an assumption up to n equals k, then the induction step to k plus 1, ending with the full conclusion. I then use the determinant of M to the n to find n equals 5 and solve for a equals 1.5. Next I find for which a the matrix has an inverse by setting det not equal to 0, then compute the inverse. I finish with two divisibility inductions, including showing difference terms are multiples of 5, 17, and 15, and I give a series induction example."}