Anyone better at math than me?

Dear lazyweb,

I’ve got a few hundred measurements like this from the prototype hardware:

input value:  0.123456,0.234567,0.345678
gives:
output value: 0.876543,0.765432,0.654321

Does anyone know how to estimate a 3×3 matrix to convert the output value to the input value? I need to do this to be able to calibrate the open-source calibration hardware that I’ve created. Thanks.