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Video: Finding the Cartesian Product of a Given Set and Itself

Kathryn Kingham

If 𝐗 = {2, 6, 7}, find 𝐗².


Video Transcript

If 𝐗 is the set two, six, seven, find 𝐗 squared.

Since 𝐗 is a nonempty set, we can multiply set 𝐗 by set 𝐗 to find 𝐗 squared. In doing so, we’re going to find the Cartesian product. We’ll set up a matrix like this. Because the set of 𝐗 contains three values, its product will be a set of nine ordered pairs.

In the first row and the first column, two, two. Next, we have two, six and then two, seven. In the second row, we’ll follow the same process: six, two; six, six; six, seven. And the third row, seven, two; seven, six; and seven, seven. And then we write out the nine of these order pairs in set form.