Lasso handling multiple variables

I would like to solve an equation that goes like this:

Y=aX1+bX2+cX3

for a huge matrix of X1,X2,X3 and Y solving for the coefficients of a,b and c. The lasso and other regularization methods are typically designed for vector input or 2 matrices with the same number of rows and columns. Does anyone has a way around it? this will be extremely useful. Using typical inverse method of d=GM causes over-fitting

Thank you. Your help is highly appreciated!

[the cyclist]

I'm confused. What are your variables like? If they are not of the same length, is it because you are missing values?

Please add more detail, and better descriptions of the variables you have. Remember, we only know the facts that you choose to share with us. Don't make us guess, which just wastes everyone's time.

[kaiba Wong]

Hi there, thank you for getting back to me. Variable X1, X2 and X3 are maps of MxN of measurements of fluid properties; whereas Y is a map of MxN of measurements of subsurface properties such as velocity. We believe that the forward modelling equation is: Y=aX1+bX2+cX3 something of this nature. Hence I tried X=[X1(:); X2(:); X3(:)] Y=Y(:) B=lasso(X,Y) doesn't work...I should be expecting 3 different coefficients for each row.. Thank you in advance