Determinant
A matrix’s determinant is the scalar value produced for a given square matrix. The determinant is dealt with in linear algebra, and it is computed using the elements of a square matrix. A determinant is a scalar value or number calculated using a square matrix. The square matrix might be 2 × 2, 3 × 3, 4 × 4, or any other form where the number of columns and rows are equal, such as n × n. If S is the set of square matrices, R is the set of integers (real or complex), and f: S → R is defined by f (A) = k, where A ∈ S and k ∈ R, then f (A) is referred to as A’s determinant. A determinant is represented by two vertical lines, i.e., |A|.
Determinant of 2×2 matrix –
[Tex]\left[\begin{matrix}a&b\\c&d\\\end{matrix}\right] = a ×d – b ×c[/Tex]
Determinant of 3×3 matrix – [Tex]\left[\begin{matrix}a&b&c\\d&e&f\\g&h&i\\\end{matrix}\right]=a(ei-fh)-b(di-gf)+c(dh-ge)[/Tex]
How to Solve a System of Equations using Inverse of Matrices?
How to Solve a System of Equations Using Inverse of Matrices? In mathematics, a matrix is an array of numbers arranged in a rectangular pattern and separated into rows and columns. They’re commonly depicted by enclosing all of the integers within square brackets.
In this article, we will discuss how to solve a system of equations using the inverse of matrices in detail.
Table of Content
- Determinant
- Minors and Cofactors
- Adjoint of a matrix
- Inverse of a matrix
- Application of Matrices and Determinants
- Representing linear systems with matrix equations
- Solving equations with inverse matrices
- Problems on How to Solve a System of Equations using Inverse of Matrices?
- Practice Problems on How to Solve a System of Equations using Inverse of Matrices?