2. Let V be an n-dimensional vector space and T: V→V be defined by T(v) = 2v. Find the kernel, range, rank, and nullity of T.

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Chapter2: Second-order Linear Odes
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2. Let V be an n-dimensional vector space and T: V → V be defined by
T(v) = 2v.
Find the kernel, range, rank, and nullity of T.
3. Let T₁: UV and T₂: V→ W be linear transformations. Show that if T20T₁ is one-to-one,
so is T₁.
Transcribed Image Text:2. Let V be an n-dimensional vector space and T: V → V be defined by T(v) = 2v. Find the kernel, range, rank, and nullity of T. 3. Let T₁: UV and T₂: V→ W be linear transformations. Show that if T20T₁ is one-to-one, so is T₁.
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