Suppose V is a 4-dimensional vector space, and that T is a linear operator on V with minimal polynomial x?. What can we say about the dimension of ker T?

Q: The kernel of a linear transformation is a vector space. O True False

A: We have to solve given problem:

Q: (Proving Linear Algebra)

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A: The solution is given as

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A: Let T be a linear operator on a two-dimensional vector space V.

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A: Let 'V' be vector space over field 'F'  Standard basis  elements of ℝ3 are given as: (1,0,0),…

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Q: (6) Suppose that T is a linear operator on a 2 dimensional vector space V and that T+ a I for any a…

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A: Consider the given information.

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A: A linear operator is called self-adjoint if T=T*.

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Q: If y is a vector space of dimension , then any set of, vectors is linearly independent. True O False

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Q: 1) Suppose that V is a finite dimensional vector space over R. Prove that every T E L(V) has an…

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A: Here the given vector space V= P4 or

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A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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Q: prove that A is invertible and A = B = C. %3D

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Q: Let T: V--&gt;W be a linear transforma­tion between finite-dimensional vector spaces V and W Let B…

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A: i uave used the definition of diagonalisation

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Q: In a vector space V, prove that Ov=0 for all ve V.

A: This quedtion from topic vector space of linear algebra.