Matematika

Pertanyaan

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2 Jawaban

  • 3x + 2y - z = 3
    -2x + y + 3z = 5
    4x - y - 2z = -1

    D = |3 2 -1| 3 2
    ........|-2 1 3| -2 1
    ........|4 -1 -2| 4 -1
    = (3.1.-2 + 2.3.4 + -1.-2.-1) - (4.1.-1 + -1.3.3 + -2.-2.2)
    = (-6 + 24 - 2) - (-4 - 9 + 8)
    = 16 - (-5)
    = 21

    Dx = |3 2 -1| 3 2
    ..........|5 1 3| 5 1
    ..........|-1 -1 -2| -1 -1
    = (3.1.-2 + 2.3.-1 + -1.5.-1) - (-1.1.-1 + -1.3.3 + -2.5.2)
    = (-6 - 6 + 5) - (1 - 9 - 20)
    = -7 - (-28)
    = 21

    Dy = |3 3 -1| 3 3
    ..........|-2 5 3| -2 5
    ..........|4 -1 -2| 4 -1
    = (3.5.-2 + 3.3.4 + -1.-2.-1) - (4.5.-1 + -1.3.3 + -2.-2.3)
    = (-30 + 36 - 2) - (-20 - 9 + 12)
    = 4 - (-17)
    = 21

    Dz = |3 2 3| 3 2
    ..........|-2 1 5| -2 1
    ..........|4 -1 -1| 4 -1
    = (3.1.-1 + 2.5.4 + 3.-2.-1) - (4.1.3 + -1.5.3 + -1.-2.2)
    = (-3 + 40 + 6) - (12 - 15 + 4)
    = 43 - 1
    = 42

    x = Dx/D = 21/21 = 1
    y = Dy/D = 21/21 = 1
    z = Dz/D = 42/21 = 2
    HP = {(1, 1, 2)}
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