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Who invented logic? A matrix is an arrangement of numbers into a rectangular form. The rows and columns can then be manipulated according to the rules of matrix addition and subtraction. Here are two matrices, a 4 x 4 (read four by four) matrix and a 3 x 4 matrix (the number of rows comes first, then the number of columns). 
How are matrices used in the real world? A computer screen is a matrix made up of pixel values. Each dot on a computer screen has a value (which tells what color and brightness to make it). They also have a particular row and position. My screen is set at a resolution of 1440 x 900, and this is just a matrix of that size. When a computer displays a picture on the screen, it modifies the values of the pixels in this matrix. Some programs use matrix mathematics to give the illusion of a moving threedimensional object on a twodimensional screen. Matrices can also have more dimensions. In the movie, The Matrix, the illusion of a 3D world was created entirely in a computer program. A basic problem using matrices. The rules for adding, subtracting and multiplying matrices can seem
complicated. For instance, how would we add these two, Each element in the first matrix is added to each element in the second to get the third. The 16 at row one and column one is added to the 4 at row one and column one of the second matrix to get 20. As long as only elements in matching locations are added, the answer will be correct. For addition to make sense, both matrices have to be of the same order (size). That is, you can't add a 3 x 3 matrix to a 3 x 4 matrix, but you could add it to another 3 x 3 matrix. Other techniques make sense of multiplication for matrices. Who invented matrices? Matrices were known and used in China more than 2000 years ago, but they didn't find application in Europe until the end of the 1600s. They were rediscovered by the Japanese mathematician Seki and the German mathematician Leibniz and were used as a tool to solve multiple linear equations. Since then, matrices have found many other uses, in economics and game theory, in code making (and breaking) and in the mathematics of quantum physics and quantum chemistry. An interesting fact about matrices. A magic square is a matrix with the following property: all the rows and columns add up to the same number. Using the rules of matrices, one magic square can be transformed into many others. Here is a magic square with the numbers one through nine where each row and each column adds up to 15:
The rules of matrices tell us we can move whole columns and rows around and not lose this property. So, we can get a 'new' magic square by switching the first and second column and then switching the top and bottom row. Here's what we get:
If you check, you will see that each row and column still adds up to 15. 
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