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In this lesson, we will learn how to find the matrix representation of dilations as geometric linear transformations.

Q1:

Consider the transformation represented by the matrix ο 3 0 0 3 ο .

What is the image of the square with vertices ( 0 , 0 ) , ( 0 , 1 ) , ( 1 , 0 ) , and ( 1 , 1 ) under this transformation?

What geometric transformation does this matrix represent?

Q2:

Describe the geometric effect of the transformation produced by the matrix ο 0 β 3 3 0 ο .

Q3:

A dilation with center the origin is composed with a rotation about the origin to form a new linear transformation. The transformation formed sends the vector ο 3 4 ο to ο β 3 3 5 6 ο .

Find the matrix representation of the transformation formed.

Find the scale factor of the original dilation.

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