Determinants Prof. I. M. El-henawy
Determinants
Definitions of Minors and a Cofactors of a Matrix
Example
Find the Minors and Cofactors of a Matrix
Definition of the A A Determinant of a Matrix
Example • Find the determinant of
Determinant of a Triangular Matrix
Conditions That Yield a Zero Determinant
Determinant of a Matrix Product
Determinant of a Scalar Multiple of a Matrix
Determinant of an Invertible Matrix
Determinant of an Inverse Matrix
Equivalent Conditions for a Nonsingular Matrix
Note that
Applications of Determinants • The Adjoint of a Matrix – Using the Adjoint of a Matrix to Find Its Inverse
• Cramer’s Rule
Solution
Cramer’s Rule
Area of a Triangle in the xy-Plane
Example
Test for Collinear Points in the xy-Plane
Two-Point Form of the Equation of a Line
Example
Volume of a Tetrahedron
Example
(2,2,5) as shown in the following Fig.
Solution
Test for Coplanar Points in Space
Three-Point Form of the Equation of a Plane
Example