linear least squares of matrices in Matlab

Given the equation of perspective projection of a set of 3D points in an image:

lambda_ij * x_ij = P_i * X_j;

how can one estimate the values of lambda_ij matrix that minimize the following linear least squares :

given that:

x_ij is 3 by n matrix

P_i is 3 by 4 matrix

and

X_j is 4 by n matrix.

I have tried

x_ij \ P_i * X_j

but this gives me a n x n matrix that I can't interpret, beacause I expect that lambda_ij shoud be a 1 x n matrix.