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Chapter 4: Q2E (page 199)

TRUE OR FALSE?

The functionT(f)=3f-4f'from C伪toC伪is a linear transformation.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Definition of a linear transformation

A linear transformation is a function from one vector space to the other vector space that respects the linear structure of each vector space.

For example,

The defining characteristic of a linear transformation.

T:V鈫�WIs that, for any vectors and y in and scalars and of the underlying fields.

T(ax+by)=aT(x)+bT(y)

02

Explanation for the given statement

Suppose that x and y are two C鈭�functions and a, b are scalars.

Tax+by=3ax+by-4ax+by'=3ax+3by-4ax'-4by'=a3x-4x'+b3y-4y'=aTx+bTy

Hence, the statement is true.

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Most popular questions from this chapter

Find the basis of all nxn diagonal matrix, and determine its dimension.

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TRUE OR FALSE?

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