Determinant of a Matrix
1 hr 28 min 12 Examples
- Quick Review of How to Calculate a Determinant
- Compute the 2×2 Determinant (Example #1)
- Compute the 3×3 Determinant (Example #2)
- Compute the 4×4 Determinant (Example #3)
- Properties of Determinants and The Invertible Matrix Theorem
- Find the Determinant using Properties of Determinants (6 Examples)
- Find the Determinant by first making a Triangular Matrix (Example #1)
- Find the Determinant by using Row Reduction Techniques (Example #2)
Cramer’s Rule
50 min 7 Examples
- Overview of Cramer’s Rule
- Solve the System using Cramer’s Rule (Examples #1 and #2)
- Application of Cramer’s Rule (Example #3)
- The Adjugate and The Inverse Formula
- Compute the Adjugate (2 Examples)
- Area and Volume using Determinants (2 Examples)
- Linear Transformations and Determinants (1 Example)
Chapter Test
1 hr 19 min 9 Problems
- True or False (Problem #1a-d)
- Find the determinant of a 5×5 matrix (Problem #2)
- Find the determinant using properties (Problem #3)
- Solve using Cramer’s Rule (Problem #4)
- Find the inverse of the 3×3 matrix by using the Adjugate (Problem #5)
- Find the area of the image of a parallelogram under the mapping (Problem #6)
- Find the volume of a parallelepiped determined by vertices (Problem #7)
- Use row reduction to find the determinant (Problem #8)
- Prove the determinant equals zero (Problem #9)
