For the sets A = {a,b} and B = {a,b,c}, determine Ax B, BX A, A2 = Ax A and B2 = BxB.
Accepted Solution
A:
Answer: Hello!the cross product between sets is defined as:if A = {a,b,c} and B = {1,2,3)then[tex]AxB = \left[\begin{array}{ccc}a\\b\\c\end{array}\right]x\left[\begin{array}{ccc}1&2&3\end{array}\right] =\left[\begin{array}{ccc}a1&a2&a3\\b1&b2&b3\\b1&b2&b3\end{array}\right][/tex]where the A took the place of the columns, and B for the files.then if our sets are A = {a,b} and B = {a,b,c)a) AxB[tex]AxB = \left[\begin{array}{ccc}aa&ab&ac\\ba&bb&bc\end{array}\right][/tex]b) BxA[tex]BxA = \left[\begin{array}{ccc}aa&ab\\ba&bb\\ca&cb\end{array}\right][/tex]c) AxA[tex]AxA = \left[\begin{array}{ccc}aa&ab\\ba&bb\end{array}\right][/tex]d) BxB[tex]BxB = \left[\begin{array}{ccc}aa&ab&ac\\ba&bb&bc\\ca&cb&cc\end{array}\right][/tex]Hope it helps, i know that is kinda hard work with this kind of operations, i tried to make a kinda of map in the first part so you can replace the values of A and B and do the multiplications by yourself, if you have troubles don't doubt of asking.