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.
Firstly, expenses are either operating expenses or non-operating expenses. Expenses incurred in operating the firm's core line of business are operating expenses. Employee wages, inventory handling costs, and expenditures for office supplies are operating expenses.