1 1 3 16 1 1 1 3 16 r 0 1 0 5 7 3 0 1 0 5 0

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Unformatted text preview: -2 12 ú 3 ê -2 -2 12 ú ê 0 -6 6 ú ® ë û®ë û ë û 1 - R2 é 1 -2 -3ù R1 + 2 R2 ® R1 é 1 0 -5ù é 1 -2 -3ù ê0 -6 6 ú ( ) 6 ê0 ú ê ú 1 -1û ® ë û ë ë0 1 -1û ® The solution to this system is x = -5 and x = -1 . [Return to Problems] It is important to note that the path we took to get the augmented matrices in this example into the final form is not the only path that we could have used. There are many different paths that we could have gone down. All the paths would have arrived at the same final augmented matrix however so we should always choose the path that we feel is the easiest path. Note as well that different people may well feel that different paths are easier and so may well solve the systems differently. They will get the same solution however. For two equations and two unknowns this process is probably a little more complicated than just the straight forward solution process we used in the first section of this chapter. This process does start becoming useful when we start looking at larger sy...
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