Not terrible.

Prompt: How would I best catalog sub-cellular organelles into a linear algebra equation?

Response: It is possible to catalog sub-cellular organelles using linear algebra, specifically by representing them as vectors and matrices.

Firstly, you could define each sub-cellular organelle as a vector with specific properties or characteristics that can be quantified. For example, the mitochondria could be represented by a vector with properties such as its size, shape, membrane potential, and ATP production rate. Similarly, the nucleus could be represented by a vector with properties such as its size, shape, DNA content, and gene expression levels.

Next, you could create a matrix that represents the relationships and interactions between different organelles in the cell. The matrix would have rows and columns representing the different organelles, with each element representing the strength or nature of the interaction between the corresponding organelles. For example, the matrix could show the strength of the interaction between the mitochondria and the endoplasmic reticulum, or between the nucleus and the Golgi apparatus.

Using this approach, you could catalog sub-cellular organelles by creating a system of linear equations that describe the properties and interactions of each organelle. By solving these equations, you could gain insights into how different organelles work together to maintain cellular function and homeostasis.

Overall, cataloging sub-cellular organelles using linear algebra can be a powerful approach for understanding the complex interactions and relationships that exist within cells. However, it is important to note that this approach would require careful consideration of the specific properties and interactions of each organelle, and the development of appropriate mathematical models to represent these characteristics.