finalsol 211 - Stony Brook University Mathematics Department Julia Viro Introduction to Linear Algebra MAT 211 Solutions for the Final Exam Problem 1

finalsol 211 - Stony Brook University Mathematics...

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Stony Brook University Introduction to Linear Algebra Mathematics Department MAT 211 Julia Viro May 15, 2008 Solutions for the Final Exam Problem 1.Solve the system using the Gauss-Jordan elimination. Verify your solution.
2 Problem 2.a)Show that skew symmetric 2×2 matrices form a subspace of the spaceM2of all 2×2matrices. Find a basis and the dimension of this subspace.b)Define the inner product inM2by< A, B >= tr(ATB)for allA, BM2. Find a basisin the orthogonal complement of the subspace of skew symmetric matrices.

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