Lesson: Matrix of a Linear Transformation

In this lesson, we will learn how to find the matrix of a linear 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:

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

Q3:

A square of area 1 undergoes a linear transformation. Given that the area of the image is also 1, what can you say about the matrix of the transformation?

AIt has determinant 1 or .
BIt is either a rotation or a reflection.
CIt preserves distances.
DIt preserves angles.

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Lesson: Matrix of a Linear Transformation

Worksheet: Matrix of a Linear Transformation • 17 Questions

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