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Chapter 2: Q8E (page 57)

Question 8: Find the inverse of linear transformation

y1=x1+7x2y2=3x1+20x2

Short Answer

Expert verified

Answer:

Inverse of the transformation isT-1(x1,x2)=(-20x1+7x2,3x1-x2) .

Step by step solution

01

Step1: System of equations

We have given a linear transformation with

y1=x1+7x2y2=3x1+20x2

02

Linear Transformation

Let T be linear transformation from R2鈫�R2.

Then, according to given equations.

Tx1x2=x1+7x23x1+20x2

03

Matrix for linear transformation

The matrix representation of T by 2x2 matrix.

.A=17320

Inverse of matrix is calculated as

First of all we will find the determinant of matrix.

A=20-21=-1adjA=20-7-31

Inverse of matrix= .A-1=-2073-1

Hence, inverse of the transformation will be

T-1(x1,x2)=(-20x1+7x2,3x1-x2)

Hence, inverse of the transformation isdata-custom-editor="chemistry" T-1(x1,x2)=(-20x1+7x2,3x1-x2)

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