Question bank: Matrix: Operations

Given the matrix A = [[1, 2], [3, 4]] and the matrix B = [[-1, 0], [2, 1]], perform the addition operation between these matrices and present the resulting matrix C. Then, perform the subtraction operation between matrix A and matrix B, and present the resulting matrix D.

Consider the matrices A = [[2, 3], [1, 4]] and B = [[-1, 2], [0, 3]]. Knowing that matrix addition and subtraction are possible operations when the matrices have the same order, determine the result of the operation A + B and A - B. Then, justify if the multiplication of matrices A and B is possible and, if so, perform the calculation of the product matrix.

Consider a company operating in the distribution and logistics sector, where inventory control and order management are crucial for operational efficiency. The company keeps a detailed record of the products in its warehouse, including information such as the type of product, supplier, receipt date, and quantity in stock. To optimize the order fulfillment process, the company has implemented a matrix-based system to keep track of product availability and facilitate logistics management. Each order placed by customers is represented by a row matrix, where each element indicates the quantity of a specific product requested. The company needs to perform matrix addition, subtraction, and multiplication operations regularly to manage its inventory and efficiently fulfill orders. A practical example of this process would be adding the matrix representing an order to the matrix controlling the inventory to check if there are enough products to meet the demand. Based on this context, solve the following questions: 1. If matrix A represents the company's current stock, with the following quantities of a single product: [[50, 20], [30, 40]], and matrix B represents a specific customer order with quantities: [[10, 5], [8, 12]], calculate the resulting matrix from the subtraction A - B and interpret the meaning of the elements of this new matrix in terms of order fulfillment. 2. Now, consider that the company receives a second order, represented by matrix C: [[15, 10], [20, 5]]. Calculate the product of matrices A and C, i.e., A * C, and explain what the elements of the resulting matrix represent in relation to inventory management.