How Do You Convert a Matrix Equation into a System of Equations?

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To convert a matrix equation into a system of equations, one must understand matrix multiplication and the representation of variables. The discussion highlights a user's struggle with matrix equations due to missed lectures and confusion over different formats. A key question raised is about the interpretation of the matrix notation, particularly the expression "[X]." Understanding these foundational concepts is essential for successfully rewriting the matrix equation as a system of equations. Clarifying these points will aid in tackling the assignment effectively.
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Homework Statement



Rewrite the following Matrix Equation as system of equations:

http://img220.imageshack.us/img220/9681/equation1111dk8.th.jpg

Homework Equations



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The Attempt at a Solution



I've been struck down with the flu for the last couple of days, so I missed 2 seemingly important Maths lectures, so I have had to rely on the online slides the lecturer put up at the end of the lectures. We are currently doing matrix equations, and have just been given an assignment on it, which is gibberish to me as all the questions are "formatted" differently if you get what I mean (Only doing Maths as it is a course requirement for one of my majors) to what is shown in the worked examples in the lecture slides.

I have chosen one of the tutorial questions from the tutorial sheet (I would've gone, but said flu screwed me over on that front again) so the above equation isn't part of the actual assignement, I just want to see the working process to figuring out the question so I can attempt the actual questions. If this against the rules, or in the wrong place, disregard topic.
 
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Well, let's see where you're at. First, do you know how to multiply matrices together?
 
pandamninator, that is about as trival a problem as you could find! I'll repeat Tom Mattson's question since it is the crucial one: What is
\left[\begin{array}{c}2 \\ -4\end{array}\right]\left[ X\right]
and what exactly do you mean by "[X]"?
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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