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

Students will be able to

Q1:

Consider the linear transformation which maps (1,1) to (3,7) and (2,0) to (2,6).

Find the matrix 𝐴 which represents this transformation.

Where does this transformation map (1,0) and (0,1)?

Q2:

Suppose the linear transformation 𝐿 sends (1,0) to (−1,5) and (1,1) to (−6,6). What is the absolute value of the determinant of the matrix representing 𝐿?

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?

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