Lecture 1 Matrices Ax combination of columns of A OR dot products of x with rows of System of linear equations Ax b Ways to think about matrix multiplication When is there a solution x When b is a linear combination of the columns of A The combinations of two of the vectors columns results in a plane With the column there is a solution when b is in the plane With the column there is a solution in the space R Identity matrices if BA I then AB I where I Multiplying matrices
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