Important Note before starting the lecture:
In the context of Gaussian elimination or other matrix row operations, you cannot directly add or subtract a scalar from an entire row. The permissible row operations are specifically designed to maintain the equivalence of the system of equations represented by the matrix. These operations are:

1- Swapping two rows.
2- Multiplying a row by a non-zero scalar.
3- Adding or subtracting a multiple of one row to/from another row.

Directly adding or subtracting a scalar from an entire row would change the solutions of the system, which is not allowed in these operations. The goal is to manipulate the system into a simpler form without altering the set of solutions it represents.






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