a) T: M, → R, where M, is the vector space ofn by n matrices over a field, and T (A) = det(A). b) T:C[0,1] → C[0,1], where C[0,1] is the vector space of real-valued functions continuous on the interval [0,1], and T(f) = df dx c) : C[0,1] → C[0,1], where C[0,1] is the vector space of real-valued functions continuous on the interval [0,1], and T (f) = f(x) +1.

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Chapter5: Inner Product Spaces
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Which of the following are linear transformations? Justify your answer.

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a) T: M, → R, where M, is the vector space ofn by n matrices over a field, and T (A) = det(A).
b) T:C[0,1] → C[0,1], where C[0,1] is the vector space of real-valued functions continuous on the interval
[0,1], and T(f) =
df
dx
c) : C[0,1] → C[0,1], where C[0,1] is the vector space of real-valued functions continuous on the interval [0,1],
and T(f) = f(x) +1.
Transcribed Image Text:a) T: M, → R, where M, is the vector space ofn by n matrices over a field, and T (A) = det(A). b) T:C[0,1] → C[0,1], where C[0,1] is the vector space of real-valued functions continuous on the interval [0,1], and T(f) = df dx c) : C[0,1] → C[0,1], where C[0,1] is the vector space of real-valued functions continuous on the interval [0,1], and T(f) = f(x) +1.
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