Linear Independence Linear Algebra

I used to be the beloved little princess of the Colobo family. Then, on my eighteenth birthday, my father brought home Sophia. She was the daughter of the old friend who had once saved his life. Out of guilt, he gave her a place in our home. Then he gave her my place too. My brother began protecting her and hating me. My childhood friend, Luca Rizzo, fell for her and left me behind. Even my father said Sophia deserved the Colobo name more than I did, though I was his biological daughter. On the day I graduated from college, they broke their promise to me for the ninety-ninth time because of her. I finally lost control. “Am I not your own daughter?” My father pulled Sophia behind him as if I were the danger, then slapped me across the face. “You jealous little thing. I should have given everything to her instead.” My brother looked at me like I was something dirty. “You don’t deserve a place in the Colobo family. Get out.” So I left. They thought I was only throwing another tantrum. They took Sophia to Switzerland to see the snow-covered mountains, certain that silence would teach me to behave. They thought I would calm down, come home, and beg for my place again. But this time, I called the research institute in Australia whose offer I had once turned down for them. “I accept,” I said. By the time the Colobo family realized I was truly gone, my phone number no longer existed. And so did Isabella Colobo.

On the day of my daughter Eleanor Baldwin's second birthday party, my entire family stood nervously by the banquet hall entrance. They were not there to greet guests, but rather to keep me from showing up and causing a scene. Mom's face was written all over with anxiety. "Lucas wouldn't actually crash the party, would he?" Dad's brow stayed tightly furrowed. "Who knows? That disgrace of a son is capable of anything." My younger brother, Cody Baldwin, had his arm wrapped gently around my wife, Kendra Clarkson, trying to reassure her. "Don't worry. If Lucas dares to show up, I'll keep you and Ellie safe." Kendra nodded slowly. "If it really comes to that... maybe we should just let Ellie be his goddaughter. At least then, we're still family..." However, the party came and went, and I never appeared. I had already made up my mind to join a classified national defense research program. Only this time, it was for good.

Everyone in the social circle of Kingsford said I was nothing more than a lapdog raised by Charles Mankin. I was always at his beck and call. I did every filthy, ludicrous thing for him under the sun. When he street raced, I rode shotgun. When he drank himself senseless, I made him hangover soup. When he chased girls, I prepared protection for them. Over time, everyone knew: Charles had a dog who never ran, never bit back, no matter how hard he kicked. They all said I must be madly in love with him. Even Charles started to believe it. So he pushed further, more freely, more cruelly, crossing lines as if they never existed. Then came my twenty-fifth birthday. He, in a rare stroke of mercy, said he'd celebrate it with me. But instead, what he got was the news that I was leaving the country. He went berserk, charging through the airport like a man possessed. I peeled his fingers off my wrist one by one, smiling like I'd never been happier. "Don't be stupid," I told him, still smiling. "That was never love." That night, Charles smashed apart his family home like a rabid dog.

Just as my wealthy boyfriend and I were talking about getting married, his mother dismissed me as an unrefined girl and demanded I attend a finishing school to learn how to be a proper wife. Looking at Zach’s pleading gaze, I gave in. I endured relentless psychological and physical torment for three months. However, on the day I was discharged, I overheard a phone call between Zach and his friend. “Zach, if you don’t want to marry Cathy, why didn’t you just tell her? Why did you have to send her to that hellhole to suffer? That finishing school your family runs is a freaking torture chamber. Constant beatings, electric shocks, forced kneeling for hours… No one comes out of there the same.” “You don’t get it. Jen is about to get engaged, and I can’t risk Cathy ruining it. As long as Jen is happy, I don’t care who I marry. Cathy grew up poor, so she can endure a little hardship. Three months of hardship for a lifetime of Stein money is a fair trade.” My vision blurred with tears when I heard those cruel words from his mouth. I thought. “Zach, since you loved Jenna so much, why did you have to toy with my feelings?”

I was six months pregnant when my husband, Michael Greene, shoved me off the edge of a yacht during a birthday party. Why? Because Lily Clement, his childhood sweetheart, had fallen into the water, and apparently, the yacht was too small for all three of us. After being pulled from the ocean, suffering from hypothermia and shock, I was taken to the hospital. Doctors determined that emergency surgery was necessary and required a family member's consent. However, no matter how many times they called, Michael never picked up. At the same time, lying in a hospital bed, I scrolled through Lily’s Instagram and saw the post she shared just hours earlier. It was a photo of the two of them, soaked but clinging to each other like lovers out of a movie. "Sometimes love comes from the most unexpected places. Thank you for always being there for me—quietly, selflessly, unshakably." That was all I needed. The day I was discharged, I left Michael a signed divorce agreement. If he wanted to be her knight in shining armor, I’d let him.

Jack Cooke—my husband, who'd never so much as scrambled an egg—suddenly went full kitchen freak. He bought a ton of pots and spatulas, then spent all day just... polishing them. When I called him out, he shrugged. "I like things clean. That a crime now?" Behind him? A mountain of dirty socks. Then it got weirder. He dragged all the kitchen stuff into our bedroom. At night, he'd get weird with a dishcloth. Like, disturbingly weird. I was done. I asked for a divorce. Jack stormed into a private dining room and shredded the papers right in front of our investors. "You're seriously ending our marriage over this? Kinda dramatic, don't you think?" I didn’t blink. “I gave up my spot for your pots and pans. A little thanks wouldn’t kill you.”

At Ryder Quinn’s kindergarten parent-child sports day, I expected my husband, Michael Quinn, to be away on a business trip. Instead, I found Michael on stage, dressed in a ballet tutu, dancing as one of the "little swans" in the fathers’ performance. I had barely taken a step forward when a little girl in a floral dress darted into his arms, calling out to him in the sweetest voice, "Daddy!" There they stood: Michael, his assistant, Janine Carter, and her daughter—all in matching family outfits. The moment our eyes met, Michael quickly pulled away from her, fumbling for an excuse. "Janine’s a single mom. It isn’t easy for her. I was just helping out." I smiled, cold and steady, and handed him the divorce papers. "Then, do me a favor too, Michael. Stop wasting my youth."

My husband's childhood sweetheart was diagnosed with a terminal illness. To fulfill her last wishes and let her experience the warmth of family, my husband, Aaron Turner, gave her my necklace. He even let her claim my birthday. Even our son started calling her "Mom" in private. He told me, "Chrishell, Sylvia is dying. Just give in to her, will you?" Whenever I asked him to spare even a little time and affection for me, our son, Lucas, would rush to speak on their behalf. "Mom, didn't you always teach me to be generous? Sylvia is dying. Why do you always make things difficult for her?" Over time, I stopped asking for anything at all. Then one night, I overheard my son speaking to his father after returning from the hospital. "Sylvia is so gentle and graceful. I wish Mom could be more like her." Aaron chuckled and affectionately brushed his hand over our son's hair. "Your mom may be a little strict, but it's all for your own good. Since you like Sylvia so much, how about we let her be your godmother?" So even the child I risked my life to bring into this world didn't like me. I lowered my gaze, quietly closed the bedroom door, and pretended none of it had happened. Since they were both filled with such regret, I'd leave quietly and give them what they wanted.

Just one week into my new job, I was wrongfully accused of cooking the books, and it cost me five years behind bars. After that, my wife found out she was pregnant. She insisted on having the baby and promised to wait for me to come home. Out of gratitude, I threw myself into work after my release. I did everything I could to give them a good life. It was until one day, I overheard a conversation between my wife and our son. “Mom, don’t let Dad come out with us. It’s embarrassing! Why did you pin Mr. Scott’s crime on him back then?! And now, the girl next door keeps making fun of me, saying my dad’s a criminal!” My wife gently pulled our son close and comforted him, saying, “I promised Mr. Scott I’d help him. Your dad’s so naive. He’ll never find out.” It turned out that my supposed happy life was nothing but lies and betrayal!

My grandfather is hit by a car, and his skull is shattered. I take the driver to court. That's when I find out my husband, Stuart Creed, who was supposedly abroad on a business trip, is suddenly at the hospital. He looks at me coldly and snaps, "Do you have any idea how important Maddy’s valedictorian announcement is? Her future can't be ruined by some car accident! Drop the case right now, or I'll cut off all your credit cards and have your grandfather kicked out of the VIP ward!" He slams the door and storms out. Before that, he snarls, "Come home when you agree. Until then, forget about calling yourself Mrs. Creed!" While I'm out desperately trying to gather money for my grandfather's surgery, a team of lawyers contacts me. Turns out the patent my grandfather once authorized to Creed Group has expired. And now, I'm the new legal owner.