DETERMINANTS Meaning and
Definition
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Determinants refer to mathematical values associated with square matrices that help determine key properties and solutions of the matrix equations. It is a scalar quantity that can be computed only for square matrices, which have an equal number of rows and columns. Determinants are extensively used in various fields of mathematics, such as linear algebra, calculus, and differential equations.
The determinant of a matrix is denoted by "det(A)" or vertical bars "|A|" enclosing the matrix. It is calculated by summing the products of each element in any row or column multiplied by its corresponding cofactor. The cofactor of any element can be found by taking the determinant of the matrix formed by deleting the row and column in which the element is located.
Determinants play a vital role in solving systems of linear equations, as they provide information on whether a system has a unique solution, infinite solutions, or no solution at all. A determinant of zero indicates that the matrix is singular, meaning it cannot be inverted or has no inverse matrix.
Furthermore, determinants also help determine the consistency of linear transformations and the orientation of objects in geometry. They are used to calculate areas and volumes of geometric shapes, as well as to determine whether a transformation changes the orientation of an object.
In summary, determinants are essential mathematical values associated with square matrices, aiding in the analysis of equations, transformations, and geometric properties.
Top Common Misspellings for DETERMINANTS *
* The statistics data for these misspellings percentages are collected from over 15,411,110 spell check sessions on www.spellchecker.net from Jan 2010 - Jun 2012.
Other Common Misspellings for DETERMINANTS
Etymology of DETERMINANTS
The word "determinants" originates from the Latin term "determinans", which is the present participle of the verb "determinare". In Latin, "determinans" means "that which determines" or "that which sets boundaries". The word was then adapted into English, retaining its original meaning. In mathematics, determinants are used to determine various properties and solutions in linear algebra, hence the name.
Similar spelling words for DETERMINANTS
- determinateness,
- determination,
- deuteromycotina,
- determinedly,
- determinism,
- determinable,
- deterministic,
- determent,
- deterrent,
- determinant,
- determining,
- determinative,
- determinist,
- determiner,
- determine,
- determinate,
- determined.
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