Hi, my name is Bassem Saad. I'm a Math Ph.D. candidate at U.C. Davis, and I'm here today for About.com to answer the question: “What is a Matrix?”A matrix is a rectangular array with rows and columns of elements or entries. These entries can be numbers, symbols, or other mathematical objects, but most likely, your matrices will only have numbers as entries. Let's take a look at an example: this is a three by two matrix; that is, it has three rows and two columns, and all its entries are real numbers. If you wanted to look at a specific entry, you would have to give its position by first saying what row it's in and then what column. For example, if I wanted to find the entry in row one, column two, I would just look over row one, column two – well, that's just two.In linear algebra, when you have a system of linear equations – in this case you have a two variable system of linear equations – you can re-write it as a matrix. I'll show you how. Here, you have a coefficient of one, so you put one. This column represents the x coefficients. Here, you have a coefficient of three for x, so I put it in the same column, just a different row. Move on to the y column. You have a coefficient of negative six, so I put a minus six. And here you have five coefficient – positive five.Here is your solution: you have zero in the solution column, and the very last equation you have one in the solution column. Now you have a matrix representing your linear system.There are whole math theories built around matrices, their properties, and uses. They include linear algebra and Representation Theory. Matrices also play an important role for differential equations, probability, physics, and engineering, but they also are in the background of your everyday life. Did you know that one of the crucial ingredients in the Google search engine comes from the study of matrices?Thanks for watching, and to learn more, visit us on the web at About.com.

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