System of equations problem?

What is x+y+z=6, x-y-z=-4, 2x+y-4z=-8 as an augmented matrix? How would you solve this using the Gauss-Jordan method?

2 Answers

Relevance
  • 6 months ago

    1  1  1 6

    1 -1 -1 -4

    2  1 -4 -8

    Add row 2 to row 1 making a new row 1, 

    then add row 3 to row 2 making a new row 2

    2 0 0 2

    3 0 -5 -12

    2 1 -4 -8

    Subtract r1 from r3 then divide r1 by 2

    1 0 0 1

    3 0 -5 -12

    0 1 -4 -10

    Multiply row 1 by -3 and add to r2

    1 0 0 1

    0 0 -5 -15

    0 1 -4 -10

    Divide r2 by -5

    1 0 0 1 

    0 0 1 3

    0 1 -4 -10

    Multiply r2 by 4 and add to r3

    1 0 0 1

    0 0 1 3

    0 1 0 2

    so x = 1, y = 2 and z = 3

  • sepia
    Lv 7
    6 months ago

    x + y + z = 6, x - y - z = -4, 2x + y - 4z = -8 

    2x = 2, x = 1,  y + z = 5, 3x - 5z = -12, z = -3

    x = 1, y = 8, z = -3

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