There is a correction needed in yesterday’s lecture: Corrections: Important note before starting the lecture: We used the ROW operations to teach you what we can do with row but be careful when using the operations and keep in mind that, 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.