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So I just started my Linear Algebra course yesterday. I am confused on one aspect. When asked to solve an augmented matrix, the teacher would employ row operations. I understand how the row operations lead from one matrix to the next, but what I don't understand is how we formulate which row operation to use. The teacher would write down R

For instance, in the picture, to get from the first matrix to the second matrix he said that R

Basically, I don't understand how he gets from the matrix to the row operations. Can someone please explain it to me?

Thanks! :)

_{2}=R_{2}+4R_{3}or something and I don't understand how he came up with this. See picture:For instance, in the picture, to get from the first matrix to the second matrix he said that R

_{2}=R_{2}-2R_{1}and that R_{3}=R_{3}-R_{1}. How does he come up with this? I'm lost eheh...Basically, I don't understand how he gets from the matrix to the row operations. Can someone please explain it to me?

Thanks! :)