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# math matrix with infinatly many solutions?

i have a matrix with infinatly many solutions. I have never solved this type before and I need a lot of help. it will end up to be a 6x12 matrix with the row reduced echlon form. but I only have 5 leading ones....please help here are the equations

1000k+100L+10m+n-100a-10b-c=0

72900p+8100q+90r+s-8100a-90b-c=0

300k+20L+m-20a-b=0

24300+180q+r-180a-b=0

60k+2L-2a=0

540p+2q-2a=0

i've put them into a rref matrix (to solve for the varibles that i need for the next step) with the form

k,l,m,n,p,q,r,s,a,b,c

What i need to do is figure out how to solve for the variables even though there are infinately many solutions...please help

### 1 Answer

- ted sLv 78 years agoFavorite Answer
hmm....I found that there were 6 leading 1's..might have not entered correctly,

...

in any case if you rref the matrix then , keeping track of which variable goes with

each column you should be able to read off how the variable associated with the 1

is written in terms of the " free " variables from the rref.....and you have [ 24300 ]

in the 4th equation...did you want that ? = - 24300 instead of 0 ?

otherwise in your 6 x 12 the last column is all zeros