Linear Algebra: Find bases for the kernel and range for the linear transformation T:R^3 to R^2 defined by T(x1, x2, x3) = (x1+x2, -2x1+x2-x3). We solve by finding the corresponding 2 x 3 matrix A, and find its null space and column span.
Several types of expenses affect profits for a business including equipment costs, inventory and facilities costs. There are two main categories for all business expenses: operating expenses and overhead expenses. The costs that fall into each category depend on the nature of the business. Essentially, operating expenses are directly related to production, while overhead expenses are the costs to run the business. Operating expenses include materials, labor and machinery used to make a product or deliver a service. For example, a soda bottler has the cost of aluminum for cans, machinery costs and labor costs.
Operating expenses can greatly impact the profitability of a business and how much cash it has. Operating expenses are the costs a company incurs that are not related to the production of a product. These expenses include items like payroll, rent, office supplies, utilities, marketing, insurance and taxes.Operating expenses are essentially the costs to keep the business running.arketing expenses are the costs of promoting products and services. Administrative expenses are the necessary expenses that are incurred in the course of running a business and are not directly tied to a specific product or service.