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Linear function standard basis.

  1. Mar 11, 2014 #1
    Does anyone know what L is? I'm trying to see if I could find videos on it on YouTube.

    On the first question this is what I think- [a;b] is a vector by the way:

    1) [2;1]c1+[7;4]c2=[1;0]
    [2;1]c1+[7;4]c2=[0;1]

    I could have also combined those two by having the linear combination equal to a size 2 identity matrix, right?! Is this correct?

    2) This is where I'm lost. I know how to switch between a standard basis and a given basis. I'm not exactly sure of the nature of the equation being asked or what it even is, including what L is.
     

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  2. jcsd
  3. Mar 16, 2014 #2
    Let me take a guess at L. From the first condition, it takes an x and transforms to a y. And from the second condition, it takes a y and transforms to a -x.

    L = \begin{bmatrix}
    0 & -1 \\
    1 & 0 \\
    \end{bmatrix}

    you can check that this L satisfies your mapping constraints.
     
  4. Mar 16, 2014 #3

    vela

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    What do you mean? The problem statement tells you what L is. It's a linear function between R2 and R2.

    Strictly speaking, what you wrote has no solution because there are no ##c_1## and ##c_2## that satisfy both equation at once. Assuming you're just being sloppy, I'd say you have the right idea.

    Not really. How can a linear combination of column vectors produce a 2x2 matrix?

    What do you mean when you say you "know how to switch between a standard basis and a given basis"?
     
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