Linear Algebra Projection Formula

My mother-in-law could not understand me. Before my business trip, I repeatedly told her not to touch anything in my study, but she mixed up the contract I needed. As a result, I lost a million-dollar order and was fired from my company. To make up for her mistake, she promised she would take care of my child and help me find another job. I froze my milk, labeled everything with notes, and gave her detailed instructions on timing and measurements. However, when my baby ended up in the hospital, I found out that she had thrown out all the milk and fed my baby expired formula instead. Even worse, she fed my baby peanuts behind my back, causing my baby to suffocate and die. Afterward, she wailed, "That was my granddaughter! How could I not care? If I could, I'd die with her..." My husband slapped me, shouting, "My mom worked so hard to take care of the child, and you want to drive her to her death? She's an old woman. It's not easy for her!" My sister-in-law came over too, calling me ungrateful and blaming me for treating an elderly woman badly. She claimed I deserved to be childless and alone. However, they did not know how many times I had stopped my mother-in-law from causing trouble and harm to them. I was driven to depression by them and eventually sent to a mental institution, where I was tortured to death. If I had the chance to do it again, I would protect my child and myself and stop preventing my mother-in-law from causing chaos for others. I would watch her bring equal destruction to each one of them!

After working overtime for half a month straight, I finally secured a contract worth more than ten million, saving the company from the brink of collapse. My boss, Richard Gray, was overjoyed. At the celebration party, he called me the pillar of the company and announced that he would reward me with a bonus. However, when the end of the month came, and I opened my payslip, I froze. Negative 250 dollars. A negative commission? I actually owed the company 250 dollars? I immediately called the finance department, asking if there was a mistake on my payslip. They replied, "No mistake. This is the cost calculation formula that Mr. Gray personally instructed us to use. He said you'd understand once you saw it." I went straight to Richard for an explanation. He laughed. "The contract that you signed, after factoring in the concessions, upfront resources, and hidden expenses, left the company with a net loss of 150 thousand. Since the loss was due to your personal decisions, you're responsible for five percent. That totals to 7500. "Considering how hard you worked, we deducted it from your base salary first. But your salary wasn't enough, so you still owe the company 250. Don't worry. The company treats its employees well. We'll write that off." Soon after, he awarded 100 thousand dollars to the newly arrived intern. I watched the newcomer, probably connected to Richard, cheerfully treat the entire company to dinner with her bonus, and something inside me just snapped. From that day onward, I did the bare minimum. I clocked in. I clocked out. Nothing more. Later, when a critical project went catastrophically wrong and the company faced a colossal compensation demand, Richard came begging me to fix it. I just smiled and said, "Sorry, Mr. Gray. I've already resigned. If there are any problems, you can ask the intern who got the 100 thousand dollar bonus to handle it."