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Chapter 4: Q42E (page 200)

TRUE OR FALSE?

42. The transformationD(f)=f'fromC鈭�toC鈭�is an isomorphism.

Short Answer

Expert verified

The solution is the statement is false.

Step by step solution

01

Explanation of the solution

Consider that the transformation is as follows.

D(f)=f'fromC鈭� toC鈭� is an isomorphism.

02

Determine whether the given transformation is one-one

Since, the derivative of constant function is zero function, which implies null space of Dis of dim1鈮�0..

Thus, the given transformationD(f)=f' is not one-to-one.

Hence, the transformationD(f)=f' fromC鈭� to C鈭�is not an isomorphism.

Thus, the given statement 鈥渢he transformation fromC鈭� toC鈭� is false.

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Most popular questions from this chapter

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphism,T(x+iy)=x2+y2from鈩� to 鈩�.

If matrix A is similar to B T(M)=AM-MBis an isomorphism from R2脳2toR2脳2

Consider linear transformation T from Vto Wand from Wto u. If ker T and ker L are both finite dimensional, and if im T = W,show that ker (LoT)is finite dimensional as well and that.

(ker (LoT)) = dim (Ker (T)) + dim (Ker (L))

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TRUE OR FALSE?

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