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Lesson: Matrix of a Linear Transformation

In this lesson, we will learn about the linear transformation such as reflections, rotations, translations, and dilations, and we will learn how to find the matrix of this transformation and how to describe it geometrically.

Worksheet: Matrix of a Linear Transformation • 17 Questions

Q1:

Consider the linear transformation which maps to and to .

Find the matrix which represents this transformation.

Where does this transformation map and ?

Q2:

The determinant of a matrix is . What is the area of the image of a unit square under the transformation it represents?

Q3:

Suppose the linear transformation sends to and to . What is the absolute value of the determinant of the matrix representing ?

Q4:

A linear transformation maps the points , , , and onto , , , and , as shown.

By finding the areas of the object and image, and considering orientation, find the determinant of the matrix representing this transformation.

Q5:

Consider the linear transformations for which , the image of , and , the image of , are unit vectors. Let be a linear transformation of this kind which has the additional property that the area of the parallelogram with vertices , , , and is as big as possible. What are the possible values of the measure of the angle between and for the transformation ?

A
B
C and
D only
E only

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