allegansveritatem
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- Jan 10, 2018
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Thanks for reply. What puzzles me here is how to set up a matrix with these components. This problem comes from the exercises after the section of the text that introduces the use of matrices. All the members of the matrices so far have been monomials. Well, I will copy the expressions here down and see what I can figure out later today.A = 0.9A + 0.05C
B = 0.1A + 0.8B
C = 0.2B + 0.95C
A + B + C = 35k
Thanks for reply. What puzzles me here is how to set up a matrix with these components. This problem comes from the exercises after the section of the text that introduces the use of matrices. All the members of the matrices so far have been monomials. Well, I will copy the expressions here down and see what I can figure out later today.
one thing I forgot to add: As yet I have not dealt with matrices with variables in the last far right column.
Here is what I did today before I read the above post from Dr Peterson:Rewrite each equation in standard form (variables on the left, constants on the right). You have presumably learned how to put that into matrix form. (And the elements of the matrix will be numbers, not monomials.)
Right. I will try to do it the manner prescribed.Please do not write 1 + 1 + 1 =3500. Please do not write such things.
I will have to work through this to make sure I understand it. Thanks.[MATH] \begin{bmatrix} 1 & 1 & 1\\ 0.1 &-0.2 & 0\\ 0 & 0.2 & -0.05 \end{bmatrix} \cdot \begin{bmatrix} A\\ B\\ C \end{bmatrix}=\begin{bmatrix} 35\\ 0\\ 0 \end{bmatrix} [/MATH]
A = 10k, B = 5k , C = 20k
I tried to put these into standard form so that I would have the variables on one side and the following is the best I could do:Rewrite each equation in standard form (variables on the left, constants on the right). You have presumably learned how to put that into matrix form. (And the elements of the matrix will be numbers, not monomials.)
I tried to put these into standard form so that I would have the variables on one side and the following is the best I could do:
View attachment 22438
But how to use these in a matrix?
Well, now that I look at it...I see what you are getting at. I don't know exactly what I was thinking...I looked at the system of equations that Skeeter suggested and, instead of replacing the A and C with 10000 and 20000 and thus seeing that they were obviously true, I somehow assumed that they had to be impossible. I knew that what I did was not what was asked for but...OK. I will go back now and do it right. Thanks for pointing it out. Sometimes in doing an exercise I get stuck in a loop of error and just don't see the elephant in the room.I see nothing there that is what I meant by "standard form (variables on the left, constants on the right)".
One example is "x + y + z = 35000".
Another is "0.1A - 0.05C = 0". To get the matrix more directly from the equation, you could write it as "0.1A + 0B - 0.05C = 0".
Perhaps you need to show us what you have learned about how to turn a system of equations into a matrix. I thought this would be the first thing they would teach you.
Isn't there a mistake in the third row of this? Shouldn't it be -.1 .2 0 0?[MATH] \begin{bmatrix} 1 & 1 & 1\\ 0.1 &-0.2 & 0\\ 0 & 0.2 & -0.05 \end{bmatrix} \cdot \begin{bmatrix} A\\ B\\ C \end{bmatrix}=\begin{bmatrix} 35\\ 0\\ 0 \end{bmatrix} [/MATH]
A = 10k, B = 5k , C = 20k
when I said "3rd row", I meant 2nd row--mainly because I have been using a matrrx with 4 rows so the equation I was referring to was my 3rd and your 2nd, sorry. And I think that it should be -.1 +.2+0 because it is derived from B= .1A +.8B. No? How could it be otherwise? I mean: B-.8B=.2B and combine that with with -.1A and you get -.1A+.2B=0. Am I wrong here?no mistake ...
the last row represents the equation [math]C = 0.2B + 0.95C \implies 0A + 0.2B - 0.05C = 0[/math]
View attachment 22480
[MATH] \begin{bmatrix} 1 & 1 & 1\\ 0.1 &-0.2 & 0\\ 0 & 0.2 & -0.05 \end{bmatrix} \cdot \begin{bmatrix} A\\ B\\ C \end{bmatrix}=\begin{bmatrix} 35\\ 0\\ 0 \end{bmatrix} [/MATH]
A = 10k, B = 5k , C = 20k