This video Contains -
00:00 - Lecture Intro
01:36 - Matrix
04:51 - Row Matrix
05:54 - Column Matrix
06:13 - Square Matrix
06:55 - Diagonal Matrix
09:51 - Scalar Matrix
10:09 - Identity Matrix
11:08 - Zero Matrix
11:30 - Upper Triangular Matrix
12:30 - Lower Triangular Matrix
13:06 - Equality Of Matrix
14:12 - Addition of Matrix
15:27 - Multiplication of Matrix by Scalar
16:10 - Multiplication of Two Matrices
22:40 - Periodic Matrix
23:32 - Idempotant Matrix
28:29 - Involutary Matrix
29:03 - Nilpotent Matrix
29:41 - Determinant Of a Matrix
33:10 - Singular Matrix
33:46 - Non-Singular Matrix
34:16 - Transpose Of a Matrix
35:00 - Orthogonal Matrix
36:40 - Theorem 1 - If A and B be n-rowed orthogonal matrices, AB and BA are also orthogonal matrices.
39:23 - Theorem 2 - If A is an orthogonal matrix, then A’ and 𝐴^(−1) are also orthogonal.
41:05 - Ex-1 - Determine the values of 𝛼,𝛽,𝛾 when [■8(0&2𝛽&𝛾@𝛼&𝛽&−𝛾@𝛼&−𝛽&𝛾)] is orthogonal.
45:11 Show that the matrix [■8(cos𝜃&sin𝜃@−sin𝜃&cos𝜃 )] is orthogonal.
46:29 Verify that the matrix 1/3 [■8(1&2&2@2&1&−2@−2&2&−1)] is orthogonal.
47:28 Symmetric Matrix
47:45 Skew Symmetric Matrix
47:55 Every square matrix can be expressed as the sum of symmetric and skew symmetric matrix.
49:29 Diagonal Elements of every Skew Symmetric matrix is always zero.
52:07 Ex-4 If A is a symmetric matrix then show that kA is also symmetric .
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Matrices | Bsc 2nd Semester | BA Bsc | Engineering Mathematics | Lecture -1 | Krishna Publication