Lesson: Matrix of Linear Transformation Mathematics

In this lesson, we will learn how to find the matrix of linear transformation and the image of a vector under transformation.

Lesson Plan

Students will be able to

perform linear transformations using matrices,
identify the matrix associated to a linear transformation,
understand determinants of linear transformations.

Lesson Explainer

Lesson Worksheet

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?