Numerical experimcnts in software celli/WI be used to verify that a set V wilh tWO
Chapter 4, Problem 40(choose chapter or problem)
Numerical experimcnts in software celli/WI be used to verify that a set V wilh tWO operations Ell and 0 is a veclOr space or a sub!;pace. Such a verification must bedone "abstractly" to take into account all possibilities for elements of V . Howcver. numerical experiments can yield counterexamples which show that V is not a vector ace or not a subspace. Use your software to verify that each of the following is 110' a subspace of M n. with the usual operations of addition of matrices and scalar multiplication:(a ) The SCt of symmetric matrices wi,h the ( I. I) entryequ:ll to 3(b) The scI of mal ri ces whose first column is [0 I ] T(c) The scI of matrices [: ~] such that lid - be I- 0
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