Why Form 8865 Reduction 2023-2024

Okay, so here we go. We have our coefficient matrix that has been augmented with our solutions. Our goal is to obtain a row reduced echelon form, where we have ones along the diagonal and zeros everywhere else. Our first step is to get a 1 in the upper left corner. If there is no 1, we may have to switch rows or multiply by a coefficient. Luckily, in this case, we already have a 1 in that position, so there is nothing to do. For the next step, we will take this 1 and pivot around it, eliminating all the other values to make them zeros. We do this by taking a value and multiplying it by 1, then adding it to each of the respective rows. For example, if we have a 2 in a certain position, we would multiply -2 by Row 1 and add it to Row 2 to make it a zero. We need to keep the equation balanced, so whatever we do to one side, we must also do to the other. After completing this step, we move on to the next row and the same operations to simplify it. If there is a way to avoid using fractions, it is preferable to do so. We can also switch rows during the row reduction process without changing the final outcome. After ing all necessary row operations, we end up with a reduced matrix. However, it is not in row reduced echelon form yet, as we need to have ones above and below the diagonal. So, our next goal is to make the element in the upper right corner a 1. We can do this by multiplying the entire row by 1/5, but we want to avoid fractions if possible. Switching rows can also be helpful...