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avatar+1348 

 

i am very confused on both of these. Thank you for help in advance

 Sep 13, 2019
 #1
avatar+104723 
+2

This will be a little lengthy.....you also need to be very careful....one mistake dooms this!!!!

 

The idea is to end up with the form 

1  0   0      a

0  1   0      b

0   0  1      c            by the use of elementary row operations

 

 

 

So the original matrix form of the equations is

 

1    3   -3      - 27

2    1    1       -2

1   -1    3       17             multiply  the first row by - 2   add to the second row

 

1    3   - 3      -27

0   -5    7       52

1    -1   3       17              multiply the first row by -1  add this to the third row

 

1    3     -3     -27

0   -5     7       52

0    -4    6       44           multiply the  second row by  3/5    add this to the first row

 

1   0     6/5     21/5

0   -5     7        52

0   -4     6        44          multiply the second row by - 4/5      add this to the third row

 

 

1   0     6/5        21/5

0   -5     7         52

0    0     2/5      12/5        multiply the  first and third rows by 5......this makes the next step easier

 

5    0     6       21             

0    -5    7       52

0    0     2       12               divide the third row by   2

 

5    0    6       21

0    -5   7      52

0   0     1        6             multply the third row by -6  add this to  the  first row

 

5     0     0    -15

0     -5   7      52

0      0    1       6              multiply the third row  by -7    add to the second row

 

5    0    0      -15

0    -5   0       10

0     0    1        6              divide the first row by   5    and the second by  -5

 

1  0    0        -3

0   1   0        -2

0   0   1         6               This is the final matrix   in Reduced-Row Echelon Form

 

Reading across.....the solution  is  { x, y, z}  =  ( -3, - 2, 6}

 

 

cool cool cool

 Sep 13, 2019
edited by CPhill  Sep 13, 2019
 #3
avatar+1348 
+1

WOW! that is a lot of info but i really appreciate taking time to hep me, i went through and double checked your work and it all looks good . This makes sense! Thank you so much .

jjennylove  Sep 13, 2019
edited by jjennylove  Sep 13, 2019
 #2
avatar+104723 
+2

Second one......this one is lacking a piece of information 

 

R1  - (1/2)R2    produces this result.....  [ 4 - (1/2)(-6), 3 - (1/2)(-3), 0 - (1/2)(12) ] =

 

[ 7, 9/2 , -6]

 

But....we don't know if we are supposed to  :

 

(1) add this result to Row 1

(2) subtract this result from Row 1  

(3) add this result to Row 2       

(4) subtract this result from Row 2

 

So.....we can't say what the transformed matrix might be ....!!!!

 

 

cool cool cool  

 Sep 13, 2019
 #4
avatar+1348 
0

 

does this example help with what your suppposed to do with it? can you help me on it now? i am super confused

jjennylove  Sep 14, 2019

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