Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.(a) The set of all vectors mapped from a vector space V into another vector space W by a linear transformation T is the kernel of T.(b) The range of a linear transformation from a vector space V into a vector space W is a subspace of V.(c) The vector spaces R3 and M3,1 are isomorphic to each other.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) The set of all vectors mapped from a vector space V into another vector space W by a linear transformation T is the kernel of T.
(b) The range of a linear transformation from a vector space V into a vector space W is a subspace of V.
(c) The vector spaces R3 and M3,1 are isomorphic to each other.

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