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Question 152176: write the system of linear equations represented by the augmented matrix. Use x,y,z and if necessary w,x,y,z for the variables.
|4 1 5 1| 6|
|1 -1 0 -1| 8|
|3 0 0 7| 4|
|0 0 11 5| 3|
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! write the system of linear equations represented by the augmented matrix. Use x,y,z and if necessary w,x,y,z for the variables.
|4 1 5 1| 6|
|1 -1 0 -1| 8|
|3 0 0 7| 4|
|0 0 11 5| 3|
Put w's after the numbers in the first column:
Put x's after the numbers in the second column:
Put y's after the numbers in the third column:
Put z's after the numbers in the fourth column:
|4w 1x 5y 1z| 6|
|1w-1x 0y-1z| 8|
|3w 0x 0y 7z| 4|
|0w 0x 11y 5z| 3|
Put in + signs between terms if there's not a
sign between them
|4w+1x+ 5y+1z| 6|
|1w-1x+ 0y-1z| 8|
|3w+0x+ 0y+7z| 4|
|0w+0x+11y+5z| 3|
Replace all the "|" after the z's with equal signs:
|4w+1x+ 5y+1z= 6|
|1w-1x+ 0y-1z= 8|
|3w+0x+ 0y+7z= 4|
|0w+0x+11y+5z= 3|
Erase all the terms with a 0 coefficient:
|4w+1x+ 5y+1z= 6|
|1w-1x -1z= 8|
|3w +7z= 4|
| 11y+5z= 3|
Erase all the 1 coefficients:
|4w+ x+ 5y+ z= 6|
| w- x - z= 8|
|3w +7z= 4|
| 11y+5z= 3|
Write as a system of equations:
Edwin
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