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Here's an image of the solution to a worked example (from Intro to Linear Algebra 4th by Strang)

here's the imgur link: http://i.imgur.com/IG6r15H.jpg

I cannot figure out what the underlined (underlining added by me) sentences mean:

"The first and last rows give x_{2}and x_{3}. Then the middle rows give x_{1}and x_{4}."

How do the middle rows only give x_{1}and x_{4}? Is this the result of treating this as a system of simultaneous equations rather than linear combinations? That's the only explanation I can find at the moment. Mostly I don't know what the author's intended meaning is.

I could find all the x's by solving simultaneous equations, but would that be how the author has done it, or has Strang found the x's a different way?

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# Solution to matrix equation

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