A community for students.
Here's the question you clicked on:
 0 viewing
suju101
 3 years ago
obtain the row rank and parametrically represented solution of the system.
3xy+3z=5
x+2y+2z3w=1
2x+5y+4z+2w=10
suju101
 3 years ago
obtain the row rank and parametrically represented solution of the system. 3xy+3z=5 x+2y+2z3w=1 2x+5y+4z+2w=10

This Question is Closed

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1augment the coeff matrix

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1row rank = colA = dimA = number of pivot points

suju101
 3 years ago
Best ResponseYou've already chosen the best response.0i didn't understand any of that.

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1then you really need to review your material, or ask more probing questions

suju101
 3 years ago
Best ResponseYou've already chosen the best response.0what exactly is row rank?

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1make sure each equation HAS the same variables; whatevers missing put a 0 to it so that it is included 3x 1y+3z+0w=5 1x+2y+2z3w=1 2x+5y+4z+2w=10 strip off everything thats NOT a number 3 1 3 0 5 1 2 2 3 1 2 5 4 2 10 now this is a coeff matrix that you can augment

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1row rank is the number of nonzero rows that you end up with

Hershey_Kisses
 3 years ago
Best ResponseYou've already chosen the best response.5i was about to say this........

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1if we format this for the wolf, life gets a bit easier :) rref{{3, 1, 3, 0, 5},{1, 2, 2, 3, 1},{2, 5, 4, 2, 10}}

suju101
 3 years ago
Best ResponseYou've already chosen the best response.0ok i got that. what's next?

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1there are 3 nonzero rows; so row rank = 3 the last column of the augmented matrix is a constant vector the next to last is the a free variable column

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1our parametric is based on these last 2 columns in this case; our constant vector and our free vectors

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1\[\vec x=\begin{pmatrix}x\\y\\z\\w \end{pmatrix}=\begin{pmatrix}109/3\\12\\92/3\\0\end{pmatrix}+w\begin{pmatrix}73/3\\8\\65/3\\1 \end{pmatrix}\]

suju101
 3 years ago
Best ResponseYou've already chosen the best response.0in this typa of questions, i was taught to suppose an arbitary constant and then calculate values of x,y,z,w for a particular value of arbitary constant.

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1yes, in this case the free variable is what you are calling an arbitrary constant

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1the augmented matrix produces our vectors for us; by augmenting with the "=" column vector to begin with we produce a particular value vector; and all thos coumns that dont stand on a "1" are called free variables ... arbitrary constants

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1it means that the rest of it can be defined using just those column vectors
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.