MAT 310 Midterm: MAT 310 SBU Fall12 PMidtermI
31 Jan 2019
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Document Summary
The actual midterm will consist of six problems. Problem 1 if u and w are subspaces of a linear space:f, show that u w need not be a subspace. However, if u w is a subspace, show that either u w or w u. V be linear maps such that : v v is an isomorphism. Show that is one-to-one (injective) and is onto (surjective). W be a linear map of nite-dimensional linear spaces and let. Problem 5 a linear map : v v is idempotent if = . Show that if is idempo- tent then acts as the identity on range(v). (such linear maps are called projections: projects v onto range(v). ) Problem 6 determine whether or not {(1, 1, 0), (2, 0, 1), ( 3, 1, 1)} is a basis for r3. Problem 7 : v v is nilpotent of order 2 if 2 is the zero endomorphism.
