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Chapter 4: Q19E (page 199)

The functionTM=detM from鈩�2脳2 to鈩� is a linear transformation.

Short Answer

Expert verified

The claim is false.

Step by step solution

01

Given in the question.

The claim is that the functionTM=detM from鈩�2脳2 to鈩� is a linear transformation.

02

Show that the function TM=detM is in linear transformation.

By definition if Tis linear then write as follows:

TM1+M2=detM1+M2for alldata-custom-editor="chemistry" A in鈩�2脳2 , but we know this is not true by the way we calculate the determinant.

Thus, the claim is false.

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Most popular questions from this chapter

Define an isomorphism fromP3 to R2脳2.

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphism,T(M)=M[2003]-[3004]M from 鈩�2脳2迟辞鈩�2脳2to .

Let V be the space of all infinite sequences of real numbers. See Example 5. Which of the subsets of given in Exercises 12 through 15 are subspaces of V ? The arithmetic sequences [i.e., sequences of the form(a,a+k,a+2k,a+3k,...) , for some constants and K .

Find a basis of a linear space and thus determine its dimension. Examine whether a subset of a linear space is a subspace. Which of the subsets of P2given in Exercises 1throughare subspaces of P2 (see Example)? Find a basis for those that are subspaces, {p(t):p'(1)=p(2)}(p'isthederivative.)

T denotes the space of infinity sequence of real numbers,T(f(t))=f(t2)from PtoP.
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