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Chapter 2: Q18 E (page 97)

Decide whether the linear transformations in Exercises 16 through 20 are invertible. Find the inverse transformation if it exists. Do the computations with paper and pencil.

y1=x2y2=x3y3=x1

Short Answer

Expert verified

The inverse of the linear transformationy1=x2y2=x3y3=x1 exits. The inverse transformation is x1=y3x2=y1x3=y2

Step by step solution

01

The System of the Linear Transformation

We have given the system of the equation of linear transformation which isy1=x2y2=x3y3=x1 .

02

Invertible functions

A function Tfrom Xto Yis called invertible if the equation T(x)=yhas a unique solution.

In this case, the inverse T-1 from Yto Xis defined by,

T-1y=The uniquexinXsuch thatTx=y

03

Checking if invertible or not

The given system of linear equations is written as,

y1=x2y2=x3y3=x1

It can also be written as

x1=y3x2=y1x3=y2

Thus, the inverse of linear transformation exits.

Hence, the inverse transformation is x1=y3x2=y1x3=y2.

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