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I would like to see how this context of matrix multiplication is played out in Differential Equations. I am starting Linear Systems, and what is a tripping up factor is the matrix multiplication. Could someone recommend a source or illustrate how to multiply matrices because the linear algebra book I have does it using a calculator, and numbers; however, I am dealing with functions?

\begin{align}\frac{d}{dt}\begin{pmatrix}5e^t\cos(t)\\ e^t(3\cos(t)-\sin(t))\end{pmatrix}&=\begin{pmatrix}-2 & 5\\-2&4\end{pmatrix}\begin{pmatrix}5\cos (t)\\ 3\cos(t)-\sin(t)\end{pmatrix}e^t\end{align}

Jose M Serra
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  • See Elementary Differential Equations with Linear Algebra by Finney and Ostberg – J. W. Tanner Apr 17 '20 at 17:30
  • There are also many video lectures you could listen to. For instance during Herb Gross's video series or youtubers like PatrickJMT. – JMoravitz Apr 17 '20 at 17:32
  • The multiplication is the same regardless of the entries in the matrix. If you can multiple matrices of integers, and you can multiply two functions, then you can multiply two matrices of functions. – pancini Apr 17 '20 at 17:32
  • @ElliotG The book doesn't show how to do it it shows how to do it with plugging it into a calculator particularly a TI-83 – Jose M Serra Apr 17 '20 at 17:33
  • Enlighten post the matrices...it's better// you will get better answer with an ecample – user577215664 Apr 17 '20 at 17:35
  • I'm confused. Are you trying to learn 1) how to multiply matrices by hand, 2) how to multiply matrices of numbers on a calculator, 3) how to multiply matrices of functions on a calculator, or some combination of all three? – pancini Apr 17 '20 at 17:37
  • @ElliotG Yes How to do that example. – Jose M Serra Apr 17 '20 at 17:40
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    @Aryadeva I added my example its a ODE that is matrix form that got solved, and I had to verify the solution which is plugged in and it works. Its just I am going to have more problems and different dimension matrices so I figured how to multiply them would be handy. – Jose M Serra Apr 17 '20 at 17:41
  • @ElliotG As I understand, the OP had only a minor introduction to matrices and had only learned how to manipulate them with calculator assistance. Having progressed through other courses and matrices became necessary again, the OP finds they are missing the prerequisite knowledge of how to utilize them. The current context the OP hopes to use them for in a current course would involve entries in the matrix who are functions, but is missing the knowledge of how to perform the operations by hand even if it were a more elementary example and the entries were instead simple integers. – JMoravitz Apr 17 '20 at 17:42
  • Enlighten thats better I voted to reopen the question – user577215664 Apr 17 '20 at 17:44
  • The end result is, as alluded to already, that you (the OP) should go back and learn how to multiply simpler matrices by hand first using textbooks aimed at building that skill or using one of the other resources suggested so far. Once you know how to multiply matrices with integers as entries, multiplying matrices with anything as entries is done exactly the same way. Don't get panicked because the entries are no longer integers. The exact same process works just like before. – JMoravitz Apr 17 '20 at 17:47
  • I disagree with reopening as the linked question (and other resources) should already cover the necessary information. Tailoring the explanation to cover very specifically the very specific matrix multiplication the OP has written is unnecessary as the end goal is to learn how to do it for any matrix multiplication, which the other resources should already cover in full detail. – JMoravitz Apr 17 '20 at 17:48
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    Actually I found a good useful book the course uses, and the videos are helpful thanks everyone. – Jose M Serra Apr 17 '20 at 17:57

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