# Video: Determining the Matrix That Represents a Given Set of Data

A company produces televisions with 32-inch, 42-inch, and 48-inch screens. The first table gives the number of televisions of each screen sized produced in factories A and B during January 2016. The second table gives the same information for February 2016. Express the total number of televisions of each screen size produced in the two months by factories A and B in a matrix.

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### Video Transcript

A company produces televisions with 32-inch, 42-inch, and 48-inch screens. The first table gives the number of televisions of each screen sized produced in factories A and B during January 2016. The second table gives the same information for February 2016. Express the total number of televisions of each screen size produced in the two months by factories A and B in a matrix.

Let’s take the table for January 2016 and turn it into a matrix. The first row is everything produced by factory A and the second row is everything produced by factory B. This is a two-binary matrix, expressing all of the information given in table one. And we want to add this information to the matrix created from table two.

The most important step here is making sure all the information lines up correctly. That means in the first row and the first column, we need the data for factory A at 32 inches. Moving across the row, you still want factory A, but then 42 inches and 48 inches. And do the same thing for factory B.

When we’re adding matrices together, to find the solution for the first row and the first column, we add the two values in that position: 820 plus 560 equals 1380. In the first row and the second column, 770 plus 550 equals 1320. Now, the first row the third column, 500 plus 830 equals 1330. Moving down to the second row and the first column, 690 plus 520 equals 1210. Second row second column, 660 plus 700 equals 1360. Second row third column equals 620 plus 660, 1280.

This is our solution matrix. It’s useful because it keeps the data about each-factory and each-size TV together.