How to Make a Bayesian Inference with a Bivariate Prior and a Univariate Likelihood

I'm trying to model a recursive Bayesian estimation, where my prior is a bivaraite Gaussian distribution and my likelihood a univariate Gaussian. I had some questions about the best way to create and combine my probability distributions.

I'm coding my bivariate prior as follows:

x1=[0:.1:6];
x2=[0:.1:6];
[X,Y] = meshgrid(x1,x2);
prior = mvnpdf([X(:) Y(:)],[3,3],[1 0;0 1]);
prior = reshape(prior,length(x1),length(x2));

And my univariate likelihood as:

x=[0:.1:6];
likelihood = normpdf(x,1,1);

I'm not quite sure how to multiply these for a correct Bayesian update. Should I multiply my likelihood pdf vector with a particular dimension of the prior pdf matrix? My prior represents the association of two stimuli with a reinforcement, and my likelihood can represent the probability of occurrence of the reinforcement in the presence of both stimuli, neither stimuli, or either stimuli.

Would it easier if I model my probability distributions by creating objects with "makedist" and "gmdistribution"?

Thank you!!