if you switch the roles of a and b you introduce a negative sign Lecture 3 Review Cross product Application of cross products Matrix 1x3 row vector 3x1 column vector Matrix operations Inverse Matrix Example Rules Distribution Association Linear Map A useful way to organize a collection of numbers A is an m x n matrix is a collection of numbers the entries in m rows and n columns aji is the entry in the ith row and the jth column scalar multiplication matrix addition transpose Matrix multiplication Identity matrix If A is mxm and B is mxm with AB I and BA I then we say B A is the inverse matrix of A Not all matrices are invertible Rotation by 2 x y y x another rotation by 2 y x x y Expressing this via matrices and Rotating by 2 is the same as multiplying by Rotating by is the same as multiplying by
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