How to do this question , in relations to transformation?

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1 Answer
Feb 2, 2018

(-6, 7)

Explanation:

I am not sure what your preferred convention is for this, but we can represent the linear transformation by right multiplication by a suitable 2 xx 2 matrix as follows:

Since we are given the images of the units (1, 0) and (0, 1) we can write our transformation as right multiplication by the matrix whose rows are the images of those points, namely:

((2, -1), (-2, 5))

So:

(1, 0)((2, -1), (-2, 5)) = (2, -1)

(0, 1)((2, -1), (-2, 5)) = (-2, 5)

Then:

(-2, 1)((2, -1), (-2, 5)) = (-6, 7)

Alternatively, we can use left multiplication of column vectors by a matrix like this:

((2, -2), (-1, 5))((1), (0)) = ((2), (-1))

((2, -2), (-1, 5))((0), (1)) = ((-2), (5))

((2, -2), (-1, 5))((-2), (1)) = ((-6), (7))

Using either convention, we find the image of (-2, 1) is (-6, 7)