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det

Represents the determinant operation in linear algebra, used to calculate a scalar value from a square matrix.

Overview

Essential in linear algebra and matrix theory for analyzing linear transformations, solving systems of equations, and finding eigenvalues.

  • Commonly used in advanced mathematics, physics, and engineering applications
  • Helps determine matrix invertibility and solve linear systems
  • Appears frequently in coordinate transformations and volume calculations
  • Distinguished from regular text by automatic proper spacing and upright formatting in mathematical contexts

Examples

Finding the determinant of a 2x2 matrix.

det⁡(abcd)=ad−bc\det\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc 
\det\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc

Calculating the determinant of a matrix with variables.

det⁡(A)=det⁡(xyzw)\det(A) = \det\begin{pmatrix} x & y \\ z & w \end{pmatrix} 
\det(A) = \det\begin{pmatrix} x & y \\ z & w \end{pmatrix}

Using determinant in a system of linear equations.

If det⁡(A)=0, then the system Ax=b has no unique solution\text{If } \det(A) = 0 \text{, then the system } Ax = b \text{ has no unique solution} 
\text{If } \det(A) = 0 \text{, then the system } Ax = b \text{ has no unique solution}