Linear Independence Linear Algebra

As soon as Danielle Bradford has recovered from her postpartum period, she brings her baby to the county clerk's office to register for the baby's birth certificate. "My baby's full name is Taylor Gardner. Her father is Matthew Gardner." The employee types on the keyboard, but his brows draw tighter afterward. "The system has flagged another child with the same name under the same father." His words leave Danielle momentarily stunned. Thinking that her ears have deceived her, she blurts out, "That's impossible! Our baby has just turned one month old!" But Danielle feels her phone buzzing in her pocket before she can finish speaking. She taps on the screen, only to see a photo sent by Matthew's assistant, Meghan Landry. In the photo, Matthew has his left arm wrapped around Meghan's waist while carrying a five-year-old boy with his right arm. The three of them stand in front of a kindergarten's entrance with smiles so bright that they practically sting Danielle's eyes. On the boy's chest is a nametag that clearly says "Taylor Gardner".

Given a new chance at life, upon learning of my husband's supposed death, the first thing I did was to register him as dead. In my previous life, after my husband, Jonah Lloyd, learned that his elder brother, Noah, had died in an accident, he resolved to assume his brother's identity and provide for his widowed sister-in-law. All because the young widow from the city couldn't withstand the gossip of the village. As for me, coming from humble origins, even without my husband, I could survive on my own. When I heard the news, I truly believed that my husband had died in an accident. I was determined to raise our daughter with all my heart. That year, during a blizzard, while his family huddled together and celebrated in the warmth, I was out there fighting over the money after selling my body. I bled out and died in the harsh, cold night. My daughter, Tina, left waiting for me to bring back good, starved to death in the bitter winter. Only after death did I learn that my husband hadn't died. He had spent his entire life in his brother's name, protecting the widow, living to see his children and grandchildren grow old around him. And now, reopening my eyes, I had returned to the very day my husband died in an accident.

After I bought my new home outright, my relatives organized a housewarming party to celebrate. During dinner, my nephew Leo suddenly said, “You’re just a spinster living alone in a huge apartment. What do you need all that space for? I happen to be getting married soon. That’s a huge deal. You should transfer the place to me. I’ll even cover the transfer fee.” I was stunned. “Are you out of your mind?” His mother Linda said, “How can you be so ungrateful? Him using your place for his newlywed life is doing you a favor. It’ll bring you good luck! Other people would jump at the chance!” The son and mother were united against me. “Anyway, tomorrow’s a great day. Grab the property deed and come with us to transfer ownership!” I rejected them without hesitation and called them crazy. Who knew they would get so furious that they would storm into my brand-new apartment and go on a rampage, smashing everything in sight. They even said smugly, “We need to show you our family doesn’t get pushed around! Go ahead and call the police! What proof do you even have that it was us?” What they did not know was that I had installed surveillance cameras on the day I moved in.

At the New Year's party, my pineapple juice is swapped for beer. To make things worse, I've just taken cephalexin, which shouldn't be mixed with alcohol. After barely surviving the ordeal, I am shocked to see my husband, Harry Grant, defending Sally Lane, who was responsible for the mix-up. "Can we please just let it go? She didn't do it on purpose," Harry pleads. However, I'm not about to forgive Sally, especially given how sketchy her relationship with my husband has always been. But Harry cuts me off with a scowl, "Enough! She's just graduated and doesn't know any better. "What's the point of holding a grudge? Do you really want to ruin her life to feel better?" he asks, clearly trying to protect her. As I watch him stand by her, my heart sinks. "Fine then, go live with her."

After returning from studying abroad, I prepared to honor my childhood betrothal. But on the very day I went to pick up my wedding gown, I saw my million-dollar couture dress worn by a poverty-stricken girl whom my fiancé had been secretly supporting. When I demanded the gown back, I was scolded as a homewrecker and mocked as a loveless hag. My fiancé excused her, saying the girl had never seen the world, and I should be more accommodating. Well, I've always loved charity. If giving away a million-dollar dress counts as charity, then fine—I'll even let go of the engagement, too. But let it be known: not just anyone can be engaged to the Vance heiress.

I marry the comatose heir of Jebony's most affluent family for the ten million dollars in wedding gifts. In the year after the wedding, I undergo 12 rounds of IVF and finally give birth to the Larkin family's successor. When our son turns five, Jacob Larkin miraculously wakes up. The media goes wild, calling me the Larkin family's lucky star. They say I'll live a life of endless privilege. I merely smile—the first look Jacob gives me after waking up is one full of disdain. He even warns me icily, "You're nothing more than a woman my father paid to bear me an heir. Don't kid yourself that I'll ever fall for you! "I grew up with Angela. If not for that accident, you would never have become my wife." I hand him the divorce papers and say calmly, "I'll step aside, then. I'll give you and Ms. Lloyd what you want."

“Mom, Dan, I received an offer from an overseas university. I plan to take it.” Lucille Shaw’s voice was soft in the silent living room, like a single drop of water rippling across a still pond. Her mother Victoria exclaimed with joy, "Really? Congratulations! When are you planning to go?" “In Ten days.”

After two years abroad in seclusion as I recovered, I received a selfie from my daughter, Lila Ashford. She was sitting on a bike, dressed in a work uniform. "Mom, you’ll be home soon, right? I miss you so much." My heart softened as I thought about how my girl had grown up. She understood that she needed to start from the bottom and work her way up. I was about to praise her when I noticed her skin seemed tanner, and her fitted shirt was the same one I’d bought her three years ago. It was frayed and worn thin, yet she still hadn’t thrown it away. As a child of the wealthiest family, Lila shouldn’t have to live like this, not even for "life experience". I zoomed in on the picture again. Her shoes were falling apart, the front gaping wide open. The more I looked, the more uneasy I became. The next second, I stumbled across Serena Ashford, my adopted daughter’s posts on social media. She was showing off male models, luxury cars, and on her wrist, the global limited-edition diamond bracelet I had given Lila. What shocked me most was the car that appeared in nearly every photo, the very one I had gifted Lila for her college graduation. How the hell had it ended up with her instead?!

It was New Year's Eve. We were streaming live when my brother called. I spoke first, "I wish you peace and a happy, long life." He gave a cold laugh. "Yeah, well, I don't want you to have any of that. I hope you spend the rest of your life in misery." I'd cut him off the year he was flat broke. Now that he was successful, this was the first thing he did—get back at me. I kept my tone calm. "I wish you peace and a happy, long life." He sounded annoyed. "Cut it out. There's no way I'm wishing you well. If I have to say something, then I hope you stay miserable forever." The host hesitated, then chimed in, "Ben, that was just a recording of Hailey's message. And yes, when she left… she was in a lot of pain and quite miserable, just like you hoped for."

I was sitting at the police station. My landlord scolded me harshly and pointed at my nose. Out of nowhere, my mother called and berated me mercilessly. “Chloe went to your place and disappeared! Did you lose her?!” “I know you’ve had grudges against me and your brother all these years, but how could you take it out on your niece?” In my previous cycle, when my mother told me Chloe was missing, I panicked and searched for her everywhere. Instead of helping, my mom and brother’s entire family dragged me to court without hesitation. I could not understand it. Chloe disappeared on her way to my place. How was that my fault? I begged the police to clear my name and review all the surveillance footage in the city. But the footage showed Chloe arriving at my door that day, and I opened the door for her. After that, she was gone, as if she had vanished into thin air. I stared blankly at the footage of her hopping cheerfully into my apartment. I had no way to explain myself. My sister-in-law lost it. She was convinced I had killed Chloe and threw boiling oil at my face in a fit of rage. I ended up in the hospital. I was disfigured and completely crushed, both physically and emotionally. No matter how hard I tried, I could not recall ever opening the door for Chloe. When I opened my eyes again, I found myself back on the day Chloe disappeared.