## Matrices

Addition Definition: If A and B are any two matrices of the same size, then the sum A+B is the matrix obtained by adding together the corresponding entries in the two matrices. Matrices of different sizes cannot be added.

Product Definition I: If A is any matrix andcis any scalar, then the productcA is the matrix obtained by multiplying each entry of A byc.

Product Definition II: If A is anmxrmatrix and B is anrxnmatrix, then the product AB is themxnmatrix whose entries are determined as follows. To find the entry in rowiand columnjof AB, single out rowifrom the matrix A and columnjfrom the matrix B. Multiply the corresponding entries from the row and column together and then add up the resulting products.

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