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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix. The process is called the *dot product* where the terms in each row of the first matrix are multiplied with the terms in each column of the second matrix.
$⎣⎢⎡ ace bdf ⎦⎥⎤ ⋅[χ_{1}χ_{2} ]=⎣⎢⎡ a⋅χ_{1}+b⋅χ_{2}c⋅χ_{1}+d⋅χ_{2}e⋅χ_{1}+f⋅χ_{2} ⎦⎥⎤ $
The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second one. For example, multiplying a $2×2$ with a $2×2$ the dimensions of the product will be $2×2$ as well.
$[25 41 ]⋅[37 32 ]=[2⋅3+4⋅75⋅3+1⋅7 2⋅3+4⋅25⋅3+1⋅2 ] $