9/18 More matrix operations.

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9/18 More matrix operations. Two useful ways to
think of matrix multiplication.
The column method The row method
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9/18 More matrix operations. How do you solve
the equation 3 x 5? How do you solve the
matrix equation A x b?
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When does a matrix A have an inverse? Want B so
so that BA I AB, where I is the identity
matrix
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Problem. Solve A x b, given the inverse of A
and b.
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Properties of inverses Transpose of a
matrix
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Interesting application The input output model
for a 2 sector economy.
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Another interesting application Use matrix
multiplication to perform row operations Scalin
g Swapping Summing