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Image of a Line Under Transformation By a Matrix

A matrix is a linear transformation, which means that it sends a line to a line.

To find the image of the lineon transformation by the matrixwe represent the line by the vectorand multiply the vector by the matrix:

From this we see that

(1)

(2)

Rearrange (1) to makethe subject and substitute into (2):

This is the image of the line.

To find the image of the lineon transformation by the matrixwe represent the line by the vectorand multiply the vector by the matrix:

From this we see that

(1)

(2)

Rearrange (1) to makethe subject and substitute into (2):

This is the image of the line.