How to add mixture Gaussian Noise to a Matrix?

I have a Matrix 'R=10*10' which represents the error of the vector 'Z=10*1'. Where the vector 'Z' contains the distances of each sensor.

so how can I add Mixture Gaussian noise to this matrix 'R'?

[KALYAN ACHARJYA]

Add the noise with R. Is there any issue?

[Khoder Makkawi]

Yes exactly that's what I need, but How can I add this mixture gaussian noise to R?

what is the formula or equation to the mixture gaussian noise?