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Multiplying Matrices, a la Shmoop. Jerry is a terrible lawn bowler and wasn't able to make the team. [Jerry running away from bowling balls]

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However, everyone who did make the team felt a little sorry for him. [Jerry crying]

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So they decided the least they could do was make him their errand boy. [Jerry looks unimpressed]

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The men and women's teams have just turned in their equipment list for the season.

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The coach tells Jerry that it costs 10 dollars per ball, two dollars per pin, and 20 dollars [Paper sheet of the costs]

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per uniform.

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What is the total cost of equipment for each team?

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Well, we know that to find the total cost for each team, we'll need to multiply the

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number of equipment by the cost.

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Remember, that if we're going to perform operations with our data, we should put our data in matrix

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format...with equipment numbers in one matrix and costs in another matrix. [Matrices of the values]

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But before we can multiply two matrices, we need to make sure that the number of columns

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in matrix A is the same as the number of rows in matrix B.

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In this case, we have 3 columns in the first matrix, and 3 rows in the second one.

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Checks out!

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To multiply the two, we'll be doing something funky.

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We'll multiply corresponding entries in the first row of matrix A and the first column

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of B...then add.

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So...the first entry in the matrix is 5 times 10 plus 20 times 2 plus 15 times 20. [Finger points to the entries in the matrix]

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And the second entry is 6 times 10 plus 15 times 2 plus 14 times 20.

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5 times 10 is 50, 20 times 2 is 40, and 15 times 20 is 300.

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So 50 plus 40 plus 300 is 390, which gives the men's team total cost of $390 for their

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equipment.

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For the women's team...we have that 6 times 10 is 60; 15 times 2 is 30 and 14 times 20 [Total cost for the mens team written in a matrix]

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is 280.

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60 plus 30 plus 280 is 370...so the women's team total cost of equipment is 370 bucks. [The cost of the women's team is added to the matrix]

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Notice that our ending matrix has dimensions of 2 by 1, which is also the row of matrix

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A and column of matrix B. If he keeps up the good work Jerry may soon be

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promoted to errand man... [Jerry cries and team mate rubs him on the back]

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