Determinant
(Redirected from Determinants)
Determinant is a mathematical concept used in linear algebra. It is a special number that can be calculated from a square matrix. The determinant helps us find the inverse of a matrix, tells us things about the matrix that are useful in systems of linear equations, calculus and more.
Definition[edit | edit source]
The determinant of a 2×2 matrix is defined as:
- det(A) = ad − bc
where:
- A = [[a, b], [c, d]]
For a 3×3 matrix, the determinant can be found by a method called "expansion by minors", or "Laplace expansion".
Properties[edit | edit source]
Determinants have some special properties, including:
- The determinant of the identity matrix is 1.
- The determinant changes sign when two rows are swapped.
- The determinant is zero if all the elements of a row or column are zero.
- The determinant is affected by row operations.
Applications[edit | edit source]
Determinants are used in a wide range of applications in mathematics and beyond, including:
- Solving systems of linear equations (Cramer's Rule)
- Calculating the inverse of a matrix
- Calculating the area or volume of a geometric shape
- In calculus, for change of variables in multiple integrals
See also[edit | edit source]
References[edit | edit source]
Determinant Resources | ||
---|---|---|
|
|
Translate to: East Asian
中文,
日本,
한국어,
South Asian
हिन्दी,
Urdu,
বাংলা,
తెలుగు,
தமிழ்,
ಕನ್ನಡ,
Southeast Asian
Indonesian,
Vietnamese,
Thai,
မြန်မာဘာသာ,
European
español,
Deutsch,
français,
русский,
português do Brasil,
Italian,
polski
Navigation: Wellness - Encyclopedia - Health topics - Disease Index - Drugs - World Directory - Gray's Anatomy - Keto diet - Recipes
Search WikiMD
Ad.Tired of being Overweight? Try W8MD's physician weight loss program.
Semaglutide (Ozempic / Wegovy and Tirzepatide (Mounjaro) available.
Advertise on WikiMD
WikiMD is not a substitute for professional medical advice. See full disclaimer.
Credits:Most images are courtesy of Wikimedia commons, and templates Wikipedia, licensed under CC BY SA or similar.
Contributors: Prab R. Tumpati, MD