video1.0<iframe src="https://www.loom.com/embed/d24eda16e7694ad08f4a14e2d991b866" frameborder="0" width="1838" height="1378" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>13781838Loomhttps://www.loom.com13781838https://cdn.loom.com/sessions/thumbnails/d24eda16e7694ad08f4a14e2d991b866-0e0c77ab68d2edba.gif4485.123I 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.