Let F be any field and consider the vector spaces F³ and F² over F. Define a F³ → F² by a(a, b, c) = (a + b + c, b + c) Then,

Question

Let F be any field and consider the vector spaces F³ and F² over F. Define a F³ → F² by
a(a, b, c) = (a + b + c, b + c)
Then, prove that a is a linear transformation and determine the matrix of a with respect to the standard basis of F³ and F².

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