### Linear Algebra Question

1. Let V be a vector space of odd dimension (greater than 1) over the real field R. Show that any linear operator on V has a proper invariant subspace other than {0}.

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1. Let V be a vector space of odd dimension (greater than 1) over the real field R. Show that any linear operator on V has a proper invariant subspace other than {0}.

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Problem attached.

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Let X be a nonempty subset of a group G. If G = <X> and H is a subgroup of G, show that H is the normal subgroup of G if and only if x^-1Hx contained in H for all x belonging to X. ALSO show that <X> is normal in G if and only if gXg^-1 contained in <X> for all g belonging to G.

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