Question

a. Many computational methods involve working with large matrices. If your computer has 8 GB of RAM, theoretically, what is the largest square (n x n) matrix of doubles your computer can hold in memory? What if you instead are storing variables of type single or int8?

b. Try creating such a (n x n) matrix of double values. What happens? What is the largest (n x n) matrix you can actually store on your machine?

Answer 1

Factors which limit addition of RAM

1) Motherboard: How much RAM can be added to your computer is motherboard dependent. If your computer was bought within last 5yrs, you must be having a motherboard which supports lots of RAM. But if the computer is older than that, there might be RAM limitation of 8GB-10GB based on the model. Modern motherboards are capable of supporting RAM upto 16GB, 32GB, 64GB or 128GB based on models.

2)  Operating system: Operating system is the other factor which restricts the amount of RAM that can be used. You need to check if the operating system installed is 32-bit or 64-bit. A 32-bit operating system can only support a maximum of 4GB. Even if additional RAM is added, the operating system can only see the 4GB and anything more won’t be detected. On the other hand, if the operating system is 64 bit, it supports 16GB minimum to upto 128GB maximum. Windows 8 Pro Edition even supports up to 512GB. The amount of RAM supported is based on which edition is installed.

3) Amount of RAM slot: If you want to add additional RAM, you need to check if additional RAM slots are available and how many. So you can decide if you want to buy a single RAM stick or multiple ones.

How much RAM in GB is needed

1GB: The latest operating system from Windows comes with a minimum RAM requirement of 1 GB. Even though the RAM is good enough to install the OS, it is going to be a frustrating experience. It will be painfully slow to open other softwares, browse internet or play games. Also it might take long time to boot to desktop. You need to add additional RAM if you are using Windows. However OS like Linux or Ubuntu works well with this much memory and you can open multiple applications without getting frustrated.

2GB: If a software recommends a certain amount of RAM as minimum requirement, always double that amount to get optimum performance. Since most application and OS comes with 1GB minimum requirement, 2GB RAM works well in most cases where you don’t use high end applications. This much RAM is enough for getting basic work done on your computer, but with limitations. This is not enough, if you are planning to run high end software like Photoshop or high end games.

4GB: This is the maximum RAM, you can have if you install 32 bit OS.4GB RAM is enough for running high end applications and games that are 32 bit. If you are using 64 bit software, adding additional RAM give you a better experience.

8GB: 8GB RAM is becoming cheaper and is default for some of the latest high end models.8GB is perfect for high end graphic designers and hard core gamers. To get the maximum result, it should be complimented with equally powerful motherboard and the processor.