Matrices and Determinant

0:00 - Introduction & Overview 0:08 - Question 13: Determinant Expansion & Factors 2:27 - Question 14: Adjoint of a 2x2 Matrix (Cos/Sin) 3:25 - Question 18: Properties of Invertible Matrices & Inverse Rules 4:45 - Question 19: Solving Determinants with Row Operations (a+b+c=0) 6:59 - Question 20: Finding x for Singular Matrices (Inverse existence) 7:52 - Question 21: System of Equations (Consistency & Unique Solutions) 10:20 - Cramer's Rule Explained (Delta1, Delta2, Delta3) 13:08 - Question 23: GP Terms (u, v, w) in a Determinant 18:23 - Question 30: Property of A * Adjoint(A) 19:48 - Question 33: Determinant Calculation with Variable Sums 21:58 - Question 24: Rotation Matrices & Orthogonal Properties 26:09 - Question 12: Possible Orders of Matrices with Prime Numbers 27:32 - Question 11: Order of Product Matrices (AB and BA) 29:45 - Question 50: Singular Matrices & Matrix Powers (A², A³) 34:12 - Matrix Entry Combinations (Distinct Matrices) 36:31 - Question 30 (Extended): Matrix Equations & Scalar Solving 41:44 - 2x2 Matrix Inverse Calculation 43:04 - Question 11: Patterns in Upper Triangular Matrix Powers (A^n) 46:04 - Question 41: Orders of AB vs. BA 47:00 - Question 13: Matrix Multiplication (3x3 by 3x1) 48:06 - Question 1: Hermitian & Skew-Hermitian Matrices 51:24 - Question 26: Confirmability for Multiplication 53:58 - Question 14: Nilpotent & Null Matrix Expressions 55:46 - Question 9: Special Matrices (Involutory, Idempotent, Nilpotent) 1:02:03 - Question 10: Non-Singular Idempotent Matrix Properties 1:05:37 - Question 8: Null Matrix Products & Identity Properties 1:09:00 - Question 6: Value of k for Singular Matrices 1:10:48 - Question 5: Determinant Expansion with Trigonometry 1:11:35 - Question 4: Matrix Equality & Distributive Laws 1:13:19 - Question 35: Commutative Properties in Matrix Algebra 1:15:54 - Question 28: Properties of Transpose (Sum & Product) 1:17:21 - Orthogonal Matrix Definition 1:17:42 - Homework Question & Closing