Changing that one number completely changes the type

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Unformatted text preview: the following fact. Fact Given any system of equations there are exactly three possibilities for the solution. 1. There will not be a solution. 2. There will be exactly one solution. 3. There will be infinitely many solutions. This is exactly what we found the possibilities to be when we where looking at two equations. It just turns out that it doesn’t matter how many equations we’ve got. There are still only these three possibilities. Now, let’s see how we can identify the first and last possibility when we are using the augmented matrix method for solving. In the previous section we stated that we wanted to use the row operations to convert the augmented matrix into the following form, é 1 0 hù ê0 1 k ú ë û é 1 0 0 pù ê0 1 0 q ú ê ú ê0 0 1 r ú ë û or depending upon the number of equations present in the system. It turns out that we should have added the qualifier, “if possible” to this instruction, because it isn’t always possible to do this. In fact, if it...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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