Matrices and Determinants: Properties and Operations
1. Determinant of a Matrix: The determinant of a matrix is equal to the determinant of its transpose.
2. Zero Row or Column: If a square matrix has a row or column of zeros, its determinant is 0.
3. Swapping Parallel Lines: Swapping two rows or columns of a square matrix changes the sign of its determinant.
4. Identical Parallel Lines: If a square matrix has two identical rows or columns, its determinant is 0.
5. Multiplying a Row/Column: Multiplying all elements of a row or column of a square matrix
Read MoreKey Concepts in Economics and Finance
Divisions of Economics
Economics is broadly divided into positive and normative economics.
Economic Theory
Economic theory is a science that studies the influence of money in the economic system. It explains facts through:
- Microeconomic Theory: Such as consumer theory.
- Macroeconomic Theory: The study of economic aggregates, units, companies, GDP (PBI), Price Index (Pc).
Economic Policy
Economic policy relates to the decision-making process involving the monetary authority (BCR) and the set of actions the
Read MoreInventory Control and Turnover
Stock Structure and Size
The total stock should consist of:
- Presentation Stock: Stock items on display in the aisle.
- Reserve Stock (Normal Cycle): Stock unlocked to meet normal customer demand between the receipt of two orders.
- Safety Stock: A protection stock that seeks to prevent the shelf from being empty because of unexpected changes in supplier supply and/or customer demand.
Inventory Management Costs
1. Acquisition Cost
The purchase price on the invoice plus all expenses paid by the buyer.
2. Storage
Read MoreTerritorial Development and Logistics in Catalonia
Equilibrium and Territorial Development: 4 Axes
4.1 Logistics Centers and Territorial Equilibrium
Logistics centers are necessary to ensure useful goods reach their destination. Due to its geographical situation, Catalonia has always been a land passage between Europe, the Iberian Peninsula, and North Africa, thus facilitating trade and the transit of goods and people.
This fact, combined with its strong industrial activity, encourages Catalonia to be a first-class logistics center in the European
Read MoreText Descriptions and Expository Writing Techniques
Understanding Text Descriptions
Defining Description
Text description aims to represent reality using words. Any description involves three basic activities related to reality:
- Name: Define the elements of reality based on perceived traits of similarity and difference to others.
- Locate: Specify the place occupied by a person or object in space and time.
- Rate: Attribute certain characteristics to what is being described.
Classes of Descriptions
There are different classes of descriptions:
1. Technical Descriptions
These
Read MoreAugustine’s Philosophy: Core Ideas Explained
Metaphysics: Creation, Ideas, and Evil
St. Augustine defends creationism: the world and time were created by God ex nihilo (from nothing). This creation is explained through the theory of Ideas: God formed concrete beings in matter based on the eternal Ideas existing in the divine mind. Furthermore, God placed seminal reasons (rationes seminales) within creation – germs of all future beings – allowing them to appear gradually over time. All created being is thus composed of matter and form. This
Read MoreStock Valuation and Return Calculation Examples
Stock Valuation Problems
NU YU Dividend Valuation
NU YU announced today that it will begin paying annual dividends. The first dividend will be paid next year in the amount of $0.57 a share. The following dividends will be $0.62, $0.77, and $1.07 a share annually for the following three years, respectively. After that, dividends are projected to increase by 3.8 percent per year. How much are you willing to pay today to buy one share of this stock if your desired rate of return is 12 percent?
Calculation
Read MoreCrane & Lifting Equipment Electrical Safety Requirements
Disconnect Switches and Contact Protection
Components must be marked with a label indicating they are protected against unintentional direct contact with live parts. If circuit disconnect switches pass through rings or busbars, they must be protected against direct contact with a minimum degree of protection of IP2X. Maintenance disconnects may be omitted if the emergency switches specified in section 4.2 are connected to the installation’s input supply. For a single crane installation, the main
Read MoreRoman Republic Officials: Key Magistracies Explained
Key Magistracies of the Roman Republic
Tribune of the Plebs
The Tribunate of the Plebs was a crucial magistracy representing the plebeians against the patricians. Tribunes held significant power, including the right to veto actions harmful to the plebeians.
Curule Aediles
The office of the Curule Aediles (initially patrician, later open to plebeians) was likely created by the Leges Liciniae Sextiae in 367 BC, alongside the existing Plebeian Aediles. The term ‘Curule’ signifies their right to sit on
Read MoreSepoy Mutiny: Causes, Results & 1858 Act Changes
Key Causes of the Sepoy Mutiny Outbreak
Four main causes for the outbreak of the Sepoy Mutiny are:
Political Cause
The reactionary policies of Lord Dalhousie caused widespread dissatisfaction among the people.
Economic Cause
The removal of the Mughal Emperor’s name from the East India Company’s coins in 1835.
Social Cause
Unrest among the royalty and common people caused by the previous century of British rule.
Religious Cause
Replacing the official Persian language with English in the administration.