Unformatted text preview: + z = 3
2 x  y  3z = 3
Let’s first write down the augmented matrix for this system. 1 2 2 ù
é3
ê 1 2
1 3ú
ê
ú
ê 2 1 3 3ú
ë
û
As with the previous examples we will mark the number(s) that we want to change in a given step
in red. The first step here is to get a 1 in the upper left hand corner and again, we have many
ways to do this. In this case we’ll notice that if we interchange the first and second row we can
get a 1 in that spot with relatively little work. 1 2 2 ù
1 3ù
é3
é 1 2
R1 « R2 ê
ê 1 2
1 3ú
1 2 2 ú
ê
ú ® ê3
ú
ê 2 1 3 3ú
ê 2 1 3 3ú
ë
û
ë
û
The next step is to get the two numbers below this 1 to be 0’s. Note as well that this will almost
always require the third row operation to do. Also, we can do both of these in one step as
follows. 1 3ù R2  3R1 ® R2 é 1 2
1 3ù
é 1 2
ê3
ú R  2 R ® R ê 0 7 5 7 ú
1 2 2 ú 3
1
3ê
ê
ú
ê 2 1 3 3ú
ê0
®
3 5 3ú
ë
û
ë
û
Next we want to turn the 7 into a 1. We can do this by dividing the second row by 7. 1 3...
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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.
 Spring '12
 MrVinh

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