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Math Help - Find a 2x3 matrix F such that FA = I

  1. #1
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    Find a 2x3 matrix F such that FA = I

    if i have

    Ax = B

    where A is a 3x2 matrix
    how do i find a 2x3 F so that FA = I?
    i thought of postmultiplying both sides by inverse of A but A is non-square XD

    i found out that its the left inverse, so far i got this

    2a - b + 3c a - b + 2c = 1 0
    2d - e + 3f d - e + 2f 0 1

    2 equations 2 unknowns?
    Last edited by experiment00; August 1st 2010 at 09:14 AM. Reason: ok...
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  2. #2
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    You haven't given us F and you haven't given us what all the variables mean, but from what I got, I think you've done the following. You have created a generic matrix F with entries a,b,c,d,e and f. And then you have found the product FA and that's what you got on the bottom.

    However, it's not 2 eqns 2 unknowns. It's 4 equations with 6 unknowns since you have a,b,c,d,e and f:

    2a -b + 3c = 1
    a -b + 2c = 0
    2d -e + 3f = 0 and
    d -e + 2f = 1
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  3. #3
    Senior Member yeKciM's Avatar
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    \displaystyle F= \begin{bmatrix}<br />
x_{11} & x_{12} & x_{13} \\<br />
x_{21} & x_{22} & x_{23} \\<br />
\end{bmatrix}

    \displaystyle A= \begin{bmatrix}<br />
y_{11} & y_{12} \\<br />
y_{21} & y_{22} \\<br />
y_{31} & y_{32} \\<br />
\end{bmatrix}

    \displaystyle I= \begin{bmatrix}<br />
1 & 0  \\<br />
0 & 1 \\<br />
\end{bmatrix}

    multiply that FA then equalize with I matrix ... equations that u get would solve ur problem i think

     FA= \begin{bmatrix} <br />
x_{11}y_{11} + x_{12}y_{21}+x_{13}y_{31} & x_{11}y_{12} + x_{12}y_{22}+x_{13}y_{32} \\ <br />
x_{21}y_{11} + x_{22}y_{21}+x_{23}y_{31} & x_{21}y_{12} + x_{22}y_{22}+x_{23}y_{32} \\<br /> <br />
\end{bmatrix}

    something like that (lol I'm sleepy can't be sure right now sorry )

    i just hope that u have let's say A matrix or F

    Edit: corrected thanks to Vlasev suggestion thanks Vlasev again
    Last edited by yeKciM; August 1st 2010 at 03:43 PM.
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  4. #4
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    yeKciM, A is a 3x2 matrix, not 2x3. But the idea is right.
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  5. #5
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by Vlasev View Post
    yeKciM, A is a 3x2 matrix, not 2x3. But the idea is right.

    hahahah... can't believe thank you (i'll fix it now )
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