Linear Independence Linear Algebra

At the dinner table, my wife's best friend suddenly speaks to her in Lytian. "Three years ago, you married Julian in a grand wedding just to help Jace get Julian's letter of forgiveness. Over the years, I've seen Julian fall more and more deeply in love with you. Yet, you're still lying to him. "You gave him sterilization pills but passed them off as his depression medication. Aren't you afraid that he'll fall apart if he finds out the truth?" My wife, Erica Inman, briefly shows a conflicted expression on her face. She then gives a bitter smile and says, "A child unwanted by their mother has no reason to be born. As long as Julian doesn't stand in the way of Jace's happiness, I will keep my promise and stay by his side for the rest of his life." No one knows that I've learned Lytian to keep up with Erica. I stand in the living room and look at the fresh kiss mark on my neck. As I glance at the medication I take regularly for my depression, my whole body turns cold. It turns out that all of Erica's affection toward me was fake. What I thought was my salvation turns out to be nothing but a carefully planned deception. Since that's the case, I'll do my part to make sure they all get what they want.

"I've transferred the three hundred-dollar rent to you. Thanks, Samuel." A contact named Misty has sent my husband, Samuel Tucker, a message on WhatsApp. I snatch his phone immediately, only to be stunned by what I see. "Rent? Samuel, you told me that this is the income you earn from your part-time job!" Samuel's expression freezes on his face. Then, he tries to snatch his phone back. "Darling, my brother has already passed away. It's difficult for Misty to raise two children on her own…" As I caress my tiny baby bump with a hand, I feel my heart sinking at his words. "Which residence is this rent for?" Samuel parts his lips hesitantly. A long time later, he finally tells me the residential area's name. I'm completely flabbergasted at that point. The luxurious apartment sitting in that particular area is an asset that my deceased parents have left for me. Also, the rent there is worth 10,000 dollars. Yet, Samuel has rented it out to my widowed sister-in-law, Misty Patterson, and her children for only 300 dollars!

Maude Ellington's fiance sends a message to his first love before their wedding. "You've always been the one I wanted to marry." With their wedding fast approaching, Maude watches him meticulously plan every detail with his first love in mind. She quietly lets it all go. Because she no longer wants the wedding. And she no longer wants him.

I was born with a rare condition. My blood carried healing properties strong enough to neutralize any poison. When Garrett Frank, the young heir from Osbury, was bitten by a venomous snake, he was hanging by a thread. In that desperate moment, I slit my wrist and used my blood to cleanse the venom from his body. Only later did I find out that whoever saved Garrett's life would become the future Mrs. Frank. But after Garrett took over the family business, the first thing he did was drain every drop of blood from my body and have me chopped up and fed to his dogs. "At that time, Loretta had already brought the antidote," he had said coldly. "If you had just waited another five minutes, I could've married her openly and honorably. "But you had to interfere. You stole her place as Mrs. Frank, drove her into despair, and pushed her to take her own life. Since you claim your blood can cure any poison, let's see how much antidote it can make." They bled me dry and threw me into a cage for his dogs. I died there, torn apart and unrecognizable. Afterward, my parents went bankrupt because of the Franks. Both of them took poison and died together. When I opened my eyes again, I was back on the very day Garrett had been bitten by the snake. Michelle Frank, Garrett's mother, looked at me with desperate hope. "I heard you have that rare healing blood," she said. "Will you please save my son?" I quickly shook my head. "That's just a rumor, Mrs. Frank. And honestly, using blood as medicine sounds pretty unsanitary. Please don't worry. I heard Ms. Huber is on her way with a special antidote. Your son will be fine!" Still, a small part of me couldn't help looking forward to what would happen. If I didn't step in this time, Garrett wouldn't just fail to inherit the family business—he'd be lucky to live another month!

After my best friend, Penny Hallmark, found herself a wealthy man, she suddenly became a different person. I had done nothing more than glance at her husband, Martin Rembrandt, yet she slapped me hard across the face. “I treated you as my closest friend, but you dared seduce Martin right in front of me. He’s Chris’s brother! Have you no shame at all?” Her accusation brought tears to my eyes, but Penny resorted to locking me inside a reservoir. “What are you playing at anyway? Fine. Let me give you something to really cry about!” I nearly drowned, and she uploaded photos of me soaked to the skin, claiming online that I was behaving indecently. I became the target of cyberbullying, my boyfriend, Christopher Rembrandt, proposed a breakup, and in utter despair, I decided to end my life. Yet my best friend mocked me coldly. “Do you really think I don’t know your little tricks? You’re just pretending to be pitiful to gain sympathy, aren’t you? “That won’t do at all, Rose. Let me give you a hand!” She pulled out my breathing tube, and only when my life completely slipped away did she smile in satisfaction. “Good. Now I can enjoy both Chris and Martin’s affection.” When I opened my eyes again, I had transmigrated into the body of Chris’s mother, who had just passed away. Given a second chance at life, I was determined to make Penny pay. After all, the man she loved most was nothing more than a hopeless mama’s boy.

Yvette Skye has been diagnosed with depression. She thinks her parents will understand her situation, but all she gets is boundless mockery and doubt. After her affair with her sister’s boyfriend is found out, she dies in an accident. After her death, her biased parents suddenly start to regret their actions.

On my wedding day, Levi Robbins' "close friend" Gina Fields suddenly fainted. Without hesitation, he dropped everything and rushed to the hospital, leaving me at the altar. My mother, witnessing this humiliating scene from her seat, suffered a heart attack. Yet, none of the guests bothered to help as they were too busy gossiping and laughing at my misfortune. By the time I managed to get her to the hospital, we had missed the critical window for treatment. Just then, Levi finally called, his voice urgent and demanding. "Caitlyn, where are you? Gina's condition is critical, and she needs your bone marrow!" "Levi, we're done," I said firmly, hanging up and walking away. This time, I would not look back.

Seven days before our wedding, Danny Wagner—my childhood sweetheart—got down on one knee for Mia Kant, the broke girl he'd been sponsoring. Right in front of me and his buddies. I didn't cry. Didn't lose it. Just slapped a smile on my face and said, "Wishing you two a lifetime of happiness." His buddies? Oh, they had the nerve to tell me to be generous and let Danny help Mia finish her "wish list." Danny, unsatisfied and ticked off, said I was overreacting and demanded an apology. Dismissive, he sneered, "I said I'd marry you after Mia's wish list was done. Stop being so unreasonable." I knew this was the last item on her list. I opened my notes app, scrolled to my wish list, and deleted all thirty-three bullet points. Done. Then I made a call. "I'm willing to marry you."

During the New Year's Eve dinner, my pineapple juice was secretly swapped for alcohol. But I had taken cephalosporin earlier on. The doctors used a lot of effort to save me, but my wife, Jennifer Robinson, shielded the person who was responsible behind her. "This matter ends here. Be generous and forgive him. He didn't do it on purpose." I didn't plan on letting this man off so easily. He had an ambiguous relationship with my wife. But Jennifer interrupted me with a frown. "That's enough! He's only a fresh graduate. What's the point of making a fuss? Do you have to ruin the rest of his life to feel satisfied?" I looked at how my wife was protecting him and my heart sank. "Then you two can spend the rest of your lives together."

The moment I find out about my pregnancy, a notification from Twitter is displayed on my phone. Apparently, it's a tweet posted by my husband, Don Romano Caliendo's childhood friend, Teresa Fiorino. "Thanks to your sperm, I get to have a child of my own during the last stage of my life." The accompanying photo is a pregnancy test that clearly states that the sperm donor is Romano. I leave a question mark in the comment section. In just half a minute, my phone begins ringing loudly. Romano's angry voice bursts from the loudspeakers immediately. I've only heard him adapt such a tone whenever he gets mad at others during family meetings. "What did you mean by that comment, Selene Gardo? Teresa is dying from cancer! All she wants is to have a baby to keep her company before she breathes her last! Don't you have any sympathy for her at all?" Before I can put down my phone, my Twitter homepage gets refreshed. This time, Teresa has uploaded another photo. It features a luxurious deluxe-style apartment, where the floor-to-ceiling windows showcase the breathtaking cityscape of Brindleport at night. The caption reads, "Thank you for giving me a home so that I don't feel lonely in my final days." In a corner of the photo, Romano can be seen crouching on the floor while piecing a baby cot together. His side profile shows how focused he is on the task. As I wipe my tears from the corners of my eyes, I silently caress my flat belly, which has yet to show any changes. I'll take you far, far away from here, my dear baby.