Recent content by Chris Rorres

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    Proving Basis of Av with Invertible A Matrix

    I need to prove that (Av1,Av2,...,Avn) spans and that it is linearly independent but this proof is so confusing to me that i don't even know where to start doing that.
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    Proving Basis of Av with Invertible A Matrix

    If A is an invertible matrix and vectors (v1,v2,...,vn) is a basis for Rn, prove that (Av1,Av2,...,Avn) is also a basis for Rn.
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    Graduate How can the inverse of a Householder matrix be verified using the given proof?

    I'm working on trying to figure this proof out but its proving to be quite difficult does anyone have any insight? Let u and w be vectors in (all real numbers)^n, and let I denote the (n × n) identity matrix. Let A= I + u(w^T), and assume that (w^T)u doesn’t equal -1 (notice that (w^T)u...
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    Graduate Suppose A^k=0 for some integer k is greater than or equal to 1

    I was wondering if anyone could give me some hints on this Suppose A^k=0 for some integer k is greater than or equal to 1. Prove that A is not invertible.