Video: Geometric Linear Transformations and Complex Numbers

A reflection in a line through the origin sends the vector [3 and 4] to [4 and 3]. Find the matrix representation of this reflection.

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Video Transcript

A reflection in a line through the origin sends the vector three, four to four, three. Find the matrix representation of this reflection.

The vector π‘₯, 𝑦 could be written as the coordinate ordered pair π‘₯, 𝑦 and can be graphed on a coordinate plane. Before the reflection, we have the point three, four. And after the reflection, we have the point four, three. And we know that it is reflected in a line that goes through the origin. This is the line 𝑦 equals π‘₯.

And a reflection in the line 𝑦 equals π‘₯ is the matrix zero, one, one, zero. This is a common matrix. And it’s good that we learn it. If we wanted to check if this was true, we could multiply it out. Three times zero plus four times one equals four. And three times one plus four times zero equals three. The matrix zero, one, one, zero represents this reflection.

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