Matrix inverse & transpose examples
❖In this video, we explore Matrix inverse & transpose examples, showing how these concepts are applied in linear algebra.
Example 1
Let A=[1 2;1 3] and B=[1 -1 2;3 2 0].
a) Find if possible, A^2 - (2A)^T.
b) Find C if (B^T + C)A^(-1) = B^T.
Example 2
Let A=[2 -2 -1;3 -1 1] and B=[1 0;1 -4;2 -5].
Find a matrix C such that CA=B^T.
Verification for Example 2
To ensure the correctness of the solution in Example 2, we confirm matrix C is correct by calculating CA and comparing it with B^T.
Whether you're learning linear algebra for the first time or looking to refresh your understanding, these examples will help solidify your knowledge of matrix operations through step-by-step solutions and clear explanations.
Video Timeline:
0:00 ❖ Introduction
0:40 ❖ Solve Example 1 part a
5:59 ❖ Solve Example 1 part b
16:34 ❖ Solve Example 2
36:22 ❖ Confirm C is correct from Example 2
41:13 ❖ Future videos
For more videos about this, you can find them in this playlist (Linear Algebra):
• Linear Algebra
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