  We found Fuchs--Garnier pairs in 3X3 matrices for the first and second
Painleve' equations which are linear in the spectral parameter. As an
application of our pairs for the second Painleve' equation we use the
generalized Laplace transform to derive an invertible integral transformation
relating two its Fuchs--Garnier pairs in 2X2 matrices with different
singularity structures, namely, the pair due to Jimbo and Miwa and the one
found by Harnad, Tracy, and Widom. Together with the certain other
transformations it allows us to relate all known 2X2 matrix Fuchs--Garnier
pairs for the second Painleve' equation with the original Garnier pair.
