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 MoreMath Formulas: Percentages, Interest, Algebra, Geometry & Statistics
Percentages
% of whole amount: part of whole / whole amount
% increase or decrease: (New / original x 100) – 100
Find % of amount: A x % / 100
% profit/loss amount: profit or loss / cost price x 100
GST Example
(GST = Amount / 11)
The total amount already includes the GST. The GST is 10% of the total excluding GST.
If we divide the total excluding GST into 10 equal amounts then:
- one of these amounts is equal to the GST and
- 11 of these amounts gives us the total including GST
Amount / 11
Simple and Compound
Read MoreMap Scale and Distance Calculations: Practical Examples
Map Scale and Distance Calculations
On a map with a scale of 1:200,000, the distance between two points is 87 mm. Calculate the actual distance on the ground:
1 mm —-> 200,000 mm
87 mm —-> x
x = 87 * 200,000 = 17,400,000 mm = 17.4 km
Expressed as a fraction, a 5 cm scale is equivalent to 20 km:
5 cm —-> 20 km
5 cm —-> 2,000,000 cm
1 cm —-> 400,000 cm. Therefore, the RSL (Representative Scale) is 1:400,000
Expressed as a fraction of English units, one inch on the scale equals
Read MoreEffective Filing Systems & Business Correspondence Essentials
Filing Systems and Business Correspondence
Consultation Agenda
- Patient Visits:
- Patient Name
- Consultation Time Allocation
- Approximate Visit Duration
- Reason for Visit
- Other Income (Telephone)
- Visits from Commercial Agents or Representatives
- Recalls
Document Filing
A file is an ordered collection of documents, both physical and digital, that are stored together. Before archiving a document, it must be organized according to a pre-defined system.
Common classification systems include:
- Alphabetical
- Numerical
- By Subject
Understanding Statistics: Key Concepts and Applications
Understanding Statistics
Statistics is a branch of mathematics and science that deals with collecting, organizing, analyzing, interpreting, and presenting data to make informed decisions. It plays a crucial role in almost every field, from business and economics to healthcare and social sciences, enabling individuals and organizations to draw meaningful conclusions and forecast future trends.
Definition of Statistics
As a Singular Noun:
Statistics refers to the science of collecting, analyzing, and
Read MoreCapacity, Layout, and Inventory Management Techniques
Capacity Management
Capacity: The maximum output a system can achieve. Understanding capacity helps align resources with demand.
Types of Capacity
Design Capacity: Theoretical maximum output.
Effective Capacity: Practical maximum output considering constraints.
Actual Capacity: Realized output under actual operating conditions.
Capacity Measures
Input Measures: Labor hours, machine hours.
Output Measures: Units produced, services delivered.
Capacity Utilization
Indicates how efficiently capacity is being