A community for students.
Here's the question you clicked on:
 0 viewing
Clarence
 one year ago
How would I go abouts solving a 3x4 matrix system?
Clarence
 one year ago
How would I go abouts solving a 3x4 matrix system?

This Question is Closed

clarence
 one year ago
Best ResponseYou've already chosen the best response.1\[\left[\begin{matrix}5 & 3 & 9 & 2 \\ 4 & 4 & 8 & 5 \\ 21 & 11 & 53 & 15\end{matrix}\right]\]

clarence
 one year ago
Best ResponseYou've already chosen the best response.1Specifically one such as above, except with a line down the middle before the last column?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\left[\begin{matrix}5 & 3 & 9 && 2 \\ 4 & 4 & 8 && 5 \\ 21 & 11 & 53 && 15\end{matrix}\right]\] like this ?

clarence
 one year ago
Best ResponseYou've already chosen the best response.1Yes, how did you manage to do that on here by the way?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1you may right click and see latex commands : dw:1440239723612:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1btw, we call it a 3x3 system the size of matrix \(A\) is \(3\times 3\) in the system of equations : \[Ax=b\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1you're just attaching that "b" also as the last column to get that 3x4 matrix that 3x4 matrix with "b" attached is called "augmented matrix"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1familiar with elimination/row opearations ?

clarence
 one year ago
Best ResponseYou've already chosen the best response.1Familiar but not well enough to solve the problem at hand unfortunately.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1first see that the solutions are not affected by row operations because you're just adding/subtracting a multiple of one row from the other... this doesn't change the solutions

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1if you have x + y = 2 x+2y = 3 then, adding one equation to other won't change the solutions because you're adding the same thing to both sides of a particular equation

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1first convince yourself that below two systems will have same solutions : system1 ``` x + y = 2 x+2y = 3 ``` system2 ``` x + y = 2 2x+3y = 5 ```

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1your goal in elimination is to get a triangular matrix

clarence
 one year ago
Best ResponseYou've already chosen the best response.1So, not 4x + 6y = 10?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1that is a valid row operation too, you're allowed to multiply entire row by a constant

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440240774738:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1you want to change the starting matrix to above form

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1start by working the element at 2,1 \[\left[\begin{matrix}5 & 3 & 9 && 2 \\ 4 & 4 & 8 && 5 \\ 21 & 11 & 53 && 15\end{matrix}\right]\] adding 4/5 times first row to second row does the job, right ?

clarence
 one year ago
Best ResponseYou've already chosen the best response.1Yes, at least I think so anyway

clarence
 one year ago
Best ResponseYou've already chosen the best response.1So now the second and third row match?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1no, what do you get after doing that first step

clarence
 one year ago
Best ResponseYou've already chosen the best response.1\[\left[\begin{matrix}5 & 3 & 9 &  2 \\ 21 & 11 & 53 & 15 \\ 21 & 11 & 53 & 15\end{matrix}\right]\]

clarence
 one year ago
Best ResponseYou've already chosen the best response.15 times the 1st row added into the 2nd row?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1yeah you could do that!

clarence
 one year ago
Best ResponseYou've already chosen the best response.1Was I not supposed to do that?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1that is not a standard method, but what you did is a better one..

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1for second step, maybe subtract second row from third row

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\left[\begin{matrix}5 & 3 & 9 &  2 \\ 21 & 11 & 53 & 15 \\ 21 & 11 & 53 & 15\end{matrix}\right]\] R3R2 gives : \[\left[\begin{matrix}5 & 3 & 9 &  2 \\ 21 & 11 & 53 & 15 \\ 0& 0& 0& 0\end{matrix}\right]\]

clarence
 one year ago
Best ResponseYou've already chosen the best response.1Okay then, what's the next step?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1next look at the element at 2,1 position you want to make it 0 so that you get a triangular matrix

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1yes how to do that using row operations ?

clarence
 one year ago
Best ResponseYou've already chosen the best response.1Multiply the 2nd row by 5 and then add 21x1st row to the second row?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Multiply the 2nd row by 5 and then "subtract" 21x1st row to the second row?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1you mean that right ?

clarence
 one year ago
Best ResponseYou've already chosen the best response.1Yes, sorry I was thinking in terms of 21

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1that works perfectly! do it

clarence
 one year ago
Best ResponseYou've already chosen the best response.1\[\left[\begin{matrix}5 & 3 & 9 & 2 \\ 0 & 8 & 76 & 33 \\ 0 & 0 & 0 & 0\end{matrix}\right]\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Looks good! so above reduced system is equivalent to : ``` 5x + 3y  9z = 2  8y  76z = 33 ```

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1let \(z=0\) and find a particular solution

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1how ? plugin \(z=0\) in the bottom equation first

clarence
 one year ago
Best ResponseYou've already chosen the best response.1Oh, I just plugged 0 in for z for both equations, my bad.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1the advantage of triangular matrix is just that solving is trivial from bottom

clarence
 one year ago
Best ResponseYou've already chosen the best response.1So y = 33/8 for the bottom solution?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1plugin z=0, y=33/8 in first equation

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1right, so our particular solution is (23/8, 33/8, 0)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1save that, we need to find nullspace

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1for nullspace, you want to solve : ``` 5x + 3y  9z = 0  8y  76z = 0 ```

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1plugin \(z=1\) and solve y, x values

clarence
 one year ago
Best ResponseYou've already chosen the best response.1x = 15/2 & y = 19/2?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Yes, so the nullspace is `t(15/2, 19/2, 1)`

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1the complete solution is given by `particular` + `nullspace`

clarence
 one year ago
Best ResponseYou've already chosen the best response.1So the one with z being 0 + what we just got?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Complete solution : ``` (23/8, 33/8, 0) + t(15/2, 19/2, 1) ```

clarence
 one year ago
Best ResponseYou've already chosen the best response.1Oh I see, that makes sense!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.