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Linear combination confusion?

  1. May 8, 2010 #1
    I have to linear equations

    3x + 2y =7 and -6x + 6y= 6

    when expressed as linear combination in column vector form they become:

    x[3,-6] + y[2,6] = [7,6]

    when solving this linear combination graphically ,First vector is plotted
    like this x=3, y=-6 and second vector is plotted like x=2, y=6 as per
    textbook

    1) first vector contains x coeffceints of equation 1 and 2. I am consfused why second element of first vector(-6) is plotted on y axis. It is x element as per equation 2. Please clarify on this why this done like
    this?
     
  2. jcsd
  3. May 8, 2010 #2

    Fredrik

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    I assume the problem is to solve the equation that you write as x[3,-6] + y[2,6] = [7,6]. Suppose you had been asked to solve the equation u[3,-6] + v[2,6] = [7,6] instead. Would that have been a different problem?
     
  4. May 13, 2010 #3

    HallsofIvy

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    In other words, the "x" and "y" used as coefficients for the vectors are NOT the "x" and "y" labeling the axes. It would, indeed, be better not to use "x" and "y" in the equation as Fredrick suggests.
     
  5. May 14, 2010 #4
    Each component of a vector can be though of as a "new axis", much like the x and y axes.
    Take a vector (a, b, c, d)
    In the coordinate system you are familiar with, a would be the x-axis value, b the y-axis, c the z-axis, d the t-axis... etc and you can go to as many axes as you want

    so even though you see an x in front of (3, -6) it does not mean that every component in that vector is on the x-axis it just means that x is some quantity multiplied by each component that lies on it's own independent axis
     
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