# Thread: Find a 2x3 matrix F such that FA = I

1. ## 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?

2. 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

3. $\displaystyle F= \begin{bmatrix}
x_{11} & x_{12} & x_{13} \\
x_{21} & x_{22} & x_{23} \\
\end{bmatrix}$

$\displaystyle A= \begin{bmatrix}
y_{11} & y_{12} \\
y_{21} & y_{22} \\
y_{31} & y_{32} \\
\end{bmatrix}$

$\displaystyle I= \begin{bmatrix}
1 & 0 \\
0 & 1 \\
\end{bmatrix}$

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

$FA= \begin{bmatrix}
x_{11}y_{11} + x_{12}y_{21}+x_{13}y_{31} & x_{11}y_{12} + x_{12}y_{22}+x_{13}y_{32} \\
x_{21}y_{11} + x_{22}y_{21}+x_{23}y_{31} & x_{21}y_{12} + x_{22}y_{22}+x_{23}y_{32} \\

\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

4. yeKciM, A is a 3x2 matrix, not 2x3. But the idea is right.

5. Originally Posted by Vlasev
yeKciM, A is a 3x2 matrix, not 2x3. But the idea is right.

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