Lost in the Array of Operations When Multiplying Matrices
Date: 03/30/2010 at 11:57:58 From: Maria Subject: getting lost in the array of operations when solving matrix When I'm solving matrices, I always have the same problem. Theoretically, I know how to solve them, but I always come up with a wrong answer. Even worse, if I repeat the same exercise, in the end I get something wrong and different from the previous mistake! I've concluded I get confused with so many operations to apply. I figured it could be a problem of concentration, but I'm not able to solve this on my own. I've tried coffee, gotten more hours of sleep, did my best to stay focused on the exercise.... Could you please help me? Thank you :) Maria
Date: 03/30/2010 at 13:04:00 From: Doctor Ian Subject: Re: getting lost in the array of operations when solving matrix Hi Maria, Can you give me an example of a matrix problem you want to solve? Often the key to dealing with lots of operations is to group them in a way that makes it easier to keep track of what's going on. For example, if you want to multiply two matrices, _ _ _ _ _ _ | 2 3 4 | | 2 | | ? | | | | | | | | 7 6 5 | | 3 | = | ? | | | | | | | |_ 3 6 9 _| |_ 5_| |_ ?_| ... you can try to remember all the individual operations -- or you can think of it this way: _ _ _ _ _ _ | 2 3 4 | | 2 | | (2 3 4) dot (2 3 5) | | | | | | | | 7 6 5 | | 3 | = | (7 6 5) dot (2 3 5) | | | | | | | |_ 3 6 9 _| |_ 5_| |_ (3 6 9) dot (2 3 5) _| Now you know everything's in the right place, so you can focus on the dot products: _ _ _ _ _ _ | 2 3 4 | | 2 | | 2*2 + 3*3 + 4*5 | | | | | | | | 7 6 5 | | 3 | = | 7*2 + 6*3 + 5*5 | | | | | | | |_ 3 6 9 _| |_ 5_| |_ 3*2 + 6*3 + 9*5 _| And you can do the same thing for matrices with other shapes: every element of the product is the dot product of a row of the first matrix and a column of the second. Even if this isn't exactly the kind of problem you're trying to solve, can you see what I'm getting at? Does it make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 03/31/2010 at 09:36:27 From: Maria Subject: Thank you (getting lost in the array of operations when solving matrix) Hi! Thank you for answering so quickly! I dind't answer sooner because I wanted to try your suggestion first. ... and it worked!!!! :) I got many more exercises right! Thank you so much. I'd also like to say that I really admire the fact that you volunteer and you give a part of your time to help people like me in this kind of subjects. There are people who volunteer in Africa and there are others like you, who volunteer in their daily life :P
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