# Matrices - Matrices A large number of engineering problems...

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Matrices

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A large number of engineering problems require the solution of large numbers of equations. These equations are often manipulated in matrix form. 58 18 7 9 3 60 9 20 9 2 72 9 7 18 1 48 4 8 4 12 = + + + = + + + = + + + = + + + z y x w z y x w z y x w z y x w = 58 60 72 48 18 7 9 3 9 20 9 2 9 7 18 1 4 8 4 12 z y x w
[ ] 1 1 3 2 4 8 4 12 48 1 4 1 8 3 4 2 12 = + + + = Row Vector Column Vector The dot product is the basic arithmetic operation in matrix algebra:

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Matrices can be multiplied if the first matrix contains the same number of columns as the second has rows. Dot products are formed from the row vectors of the first matrix and column vectors of the second. [ ] [ ] [ ] [ ] 6
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Matrices - Matrices A large number of engineering problems...

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