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matrix multiplication

Matrix Multiplication, basic strategy

 

What does it mean to multiply one matrix by another?  This is a really nice diagram that tells it all.

 

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from hem.libretexts.org

Practical Matrix Multiplication

What does all of this mean in real life?  We are taught that the number of columns in the first matrix must equal the number of rows in the second matrix.   Could this be more than a mental gymnastics right of passage for high school students?

Let us take a gal Joan that sells home made pies:  apple, black berry, and coconut

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Joan lives in western Washington State.  Apples are pretty inexpensive, black berries grow as a weed, and fresh coconut is expensive.  Joan uses spread sheets to keep track of how many pies she sells each day of the week, how much she sells them for, and how much it costs to produce them.

 

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A spread sheet from Joan’s kitchen. The first matrix has 3 columns and the second has 3 rows… we can multiply.  Price per unit  x the number of units sold is the revenue.   The cost to produce a unit times the number of units sold, the production cost takes away from the profit

Open Office Calc, the free, open source cousin of Microsoft  Excel.

MatrixMult2Let us do the math for the first and put it in B8.  It is very easy to write in the wrong formulas.  The software makes it easy to visualize what you are doing.

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In Open Office Calc, clicking on the cell with the formula reveals the cells that are acted upon and the color coded equations. It is an easy way to check for mistakes.

What is cool about these spread sheets is that they can be saved and changed and the pie business changes.  Say our pie shop owner contracts with some local high school students to harvest wild blackberries growing by the highway.  The production cost drops to $3 per pie?  The not so cool thing about these spread sheets is that entering each equation over and over is almost as PAINFUL as doing the entire beeping thing by hand, as per many high school math classes for the past few decades.

The EASY way to do Matrix Multiplication in Open Office

Open Office Calc has an easy way to calculate arrays.

  1.   In the upper left hand corner, click on the fx function key
  2. Select the MMULT function
  3. Enter the values.  A matrix in columns B to D and rows 2 to 3 would be written as B2:D3.  You don’t even have to type this in.  Simply use the left mouse key to highlight these cells on your spread sheet.
matrix multiplication in Open Office Calc
Steps to doing matrix multiplication in Open Office Calc

 

Here are the results in the finished spread sheet.  Compare the results of B12:F13 with those in B8:F9.

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The Open Office matrix multiplication function (blue highlight) gives the same results as painstakingly entering the equations one by one.

 

Microsoft Office also performs the same calculations.

 

 

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