❖ 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.