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Again, this almost always requires the third row operation. \[\require\left[ \right]\begin\ \to \end\left[ \right]\] We have the augmented matrix in the required form and so we’re done.The solution to this system is \(x = 4\) and \(y = - 1\).This means that we need to change the red three into a zero.
This is mostly dependent on the instructor and/or textbook being used.
Next, we need to discuss elementary row operations.
Before we get into the method we first need to get some definitions out of the way.
An augmented matrix for a system of equations is a matrix of numbers in which each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign) and each column represents all the coefficients for a single variable. Here is the system of equations that we looked at in the previous section.
In this part we won’t put in as much explanation for each step.
We will mark the next number that we need to change in red as we did in the previous part.
For systems of two equations it is probably a little more complicated than the methods we looked at in the first section.
However, for systems with more equations it is probably easier than using the method we saw in the previous section.
However, the only way to change the -2 into a zero that we had to have as well was to also change the 1 in the lower right corner as well. Sometimes it will happen and trying to keep both ones will only cause problems. \[\require\left[ \right]\begin\ \to \end\left[ \right]\begin\ \to \end\left[ \right]\] The solution to this system is then \(x = 2\) and \(y = 1\).
Let’s first write down the augmented matrix for this system.