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Chapter 2: Q44E (page 41)

A nonzero matrix of the form A=[a-bba] represents a rotation combined with ascaling. Use the formula derived in Exercise 2.1.13 to find the inverse of A .Interpret the linear transformation defined byA-1 geometrically. Explain.

Short Answer

Expert verified

The inverse of the matrix is,A-1=1a2+b2ab-ba ,the geometrical interpretation is,

Step by step solution

01

Compute the inverse of the matrix.

Consider the matrix.

A=a-bba

The inverse of the matrix is,

A-1=1a脳a-b脳-bab-ba鈭�A-11a2+b2ab-ba

02

Interpret the linear transformation.

The matrix A represents the rotation by an angle and scaling by a factor r .

The inverse matrix A-1 represents the rotation by an angle -胃and scaling by a factor1r .

The geometrical representation is,

03

Final answer.

The inverse matrix is, A-1=1a2+b2ab-bawith geometrical interpretation of linear

transformation is

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