Recent content by Takuya

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    Undergrad Understanding Factorials: A Combinatorics Primer

    In my combinatorics book, it's discussing inclusion-exclusion, and it says that n!-(n-1)! = (n-1)!*(n-1)! Can someone help me understand the rules of factorials? Thanks!
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    Graduate Basis for kernel of linear transform

    Ohhh right right. Yeah I was getting ahead of myself. I understand now! Thanks :)
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    Graduate Basis for kernel of linear transform

    a1=a2 and a3=a4, so that a2 and a4 can be arbitrary. So plugging back into the original L(a), and factoring, you'd get that {(1+t),(t2+t3)} is the kernel of L? The range would be … any value of a2 or a4 for t3 and t, so the range is just {t,t3} ?
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    Graduate Basis for kernel of linear transform

    Hey guys! I am having a major brain problem today, with this problem. L is a linear transform that maps L:P4\rightarrowP4 As such that (a1t3+a2t2+a3t+a4 = (a1-a2)t3+(a3-a4)t. I am trying to find the basis for the kernel and range. I know that the standard basis for P4 is...