If you use Excel to model businesses, business processes, or business transactions, this course will change your life. You’ll learn how to create tools for yourself that will amaze even you. Unrestricted use of this material is available in two ways.

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 Matrix multiplication
• A matrix is represented by a rectangular range
• An “m by n” matrix has m rows and n columns (written “mxn”)
• In a matrix product A•B, the first factor A must have as many columns as the second factor B has rows
• The product has the same number of rows as the first factor and the same number of columns as the second factor
• To multiply a 1xp matrix by a px1 matrix:
• Multiply each of the respective elements together and sum
• For different sizes, just break them up into 1xn and nx1

Matrix multiplication looks complicated. When first learning it, you might have the reaction, “What does this have to do with me?” The short answer is that it captures in a neat package a long series of complex manipulations that we would otherwise have to perform more explicitly.

By introducing the formalism of matrices, we can move our thinking to a higher level. No longer need we be concerned with specific cells and cell formulas. Matrices give us a way of manipulating blocks of data instead of a series of manipulations of cells.

Matrix Multiplication and Array Arithmetic

For many of you, matrix multiplication and array arithmetic are new ideas. It’s easy to get lost in the details of how they work and then forget about why we use them.

To keep a clear view of the forest and avoid focusing only on the trees, remember why we use matrix multiplication and array arithmetic. Briefly, we use them because we find that it’s very often helpful to decompose a problem into parts (analysis), then do calculations on the parts, and finally reassemble the final solution from the results of those partial calculations (synthesis).

Matrix multiplication and array arithmetic provide us with very convenient methods for performing those intermediate calculations on the parts. They’re the tools that make analysis and synthesis so powerful.