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Chapter 4: Q23E (page 200)

The kernel of liner transformationT(ft)=f(t2)fromPtoPis{0}.

Short Answer

Expert verified

The given statement is True

Step by step solution

01

Determine the dimension of kernel of T .

Consider a linear transformation T(f(t))=f(t2)fromPtoP.

A function Tis linear transformation on D to D if T(0)=0.

A kernel of a function Tis defined as ker (T)={fxI^P:Tfx=0} .

02

Determine whether the statement is True of false

Ifft2=0 means all the coefficient must be zero impliesft=0 .

By the definition of kernel, the dimension of kernel of T is 0.

Hence, the statement is true.

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