## Matrix Multiplication Utility |

This page contains a routine that computes the product of two matrices: [**A**] [**B**] = [**C**].

The maximum size of [**A**] and [**B**] is 12 X 12, and the elements of each are assumed to be real.

Consider the matrices [**A**] and [**B**]:

a_{11} |
a_{12} |
a_{13} |
a_{14} |
a_{15} |
||||||||

[A] |
= | a_{21} |
a_{22} |
a_{23} |
a_{24} |
a_{25} |
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a_{31} |
a_{32} |
a_{33} |
a_{34} |
a_{35} |

b_{11} |
b_{12} |
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b_{21} |
b_{22} |
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[B] |
= | b_{31} |
b_{32} |
|||

b_{41} |
b_{42} |
|||||

b_{51} |
b_{52} |

The product of these two matrices, [**A**] [**B**] = [**C**], is computed by multiplying the columns of [**B**] by the rows of [**A**]. For example,

c_{11} |
= | a_{11}*b_{11} + a_{12}*b_{21} + a_{13}*b_{31} + a_{14}*b_{41} + a_{15}*b_{51} |
||

c_{12} |
= | a_{11}*b_{12} + a_{12}*b_{22} + a_{13}*b_{32} + a_{14}*b_{42} + a_{15}*b_{52} |

and so on . . .

c_{11} |
c_{12} |
|||||

[C] |
= | c_{21} |
c_{22} |
|||

c_{31} |
c_{32} |

If [**A**] is an M X N matrix (M rows, N columns), and [**B**] is an N X P matrix (N rows, P columns), the product of these matrices, [**A**] [**B**] = [**C**], is a matrix of size M X P (M rows, P columns).

**In fact, it is important to note**: If the number of columns of [**A**] does not equal the number of rows of [**B**], the multiplication of these two matrices cannot proceed. For example, if the order of these matrices were reversed, [**B**] [**A**], the multiplication could not be done.

**HOW TO USE THIS UTILITY**

(i) The first four entries should be the dimensions of the [**A**] and [**B**] matrices: M, N, N, and P (remember, none of these values can be greater than 12).

(ii) The next M x N entries should be the coefficients of the [**A**] Matrix.

The coefficients should be entered in the following order:

a_{11}, a_{12}, a_{13}, . . .

a_{21}, a_{22}, a_{23}, . . .

etc.

(iii) The next N x P entries should be the coefficients of the [**B**] Matrix.

The coefficients should be entered in the following order:

b_{11}, b_{12}, b_{13}, . . .

b_{21}, b_{22}, b_{23}, . . .

etc.

Do not enter commas, periods, brackets, etc. Also note that numbers in scientific notation are NOT recognized.

For example, say we want to multiply matrices with the dimensions of the sample matrices presented above.

Data input to the box should have the following format:

3 | 5 | 5 | 2 | |||||

a_{11} |
a_{12} |
a_{13} |
a_{14} |
a_{15} |
||||

a_{21} |
a_{22} |
a_{23} |
a_{24} |
a_{25} |
||||

a_{31} |
a_{32} |
a_{33} |
a_{34} |
a_{35} |
||||

b_{11} |
b_{12} |
|||||||

b_{21} |
b_{22} |
|||||||

b_{31} |
b_{32} |
|||||||

b_{41} |
b_{42} |
|||||||

b_{51} |
b_{52} |

Once all the data has been entered, click the **Multiply** button, and the product matrix, [**C**], will be computed.