Linear Independence Linear Algebra

Six years after losing my memory and being taken in by the Lawson family, my husband, Jack Lawson, brought his childhood sweetheart home. She was beautiful and understanding, and everyone liked her. Not only did Jack favor her, but our two children also called her "Mom" behind my back. Due to the extreme sadness, I actually got my memories back. Since the Lawson family felt that my presence was unnecessary, then I might as well go home and be the heiress of the powerful Miller family again.

My boyfriend was the illegitimate son of Oceanfall Pack’s Alpha, while I was just an ordinary healer working at the pack’s hospital. When his father broke his legs and threw him out, I was the one who stayed and gave him everything I could. However, the day fifteen luxury cars came to take him back, he ignored me completely and left with my coworker instead. When reporters pointed at me and asked him, “Who is this Omega to you?” Jeremy said coldly, “Just my healer. Nothing more.” Later, he rose to power to become the untouchable Alpha. I turned away, crossing borders to Sirius Pack to marry his greatest rival. On the night of my mating ceremony, he sent his men to kidnap me. “Are you really going to marry Marcus Flint, a man cursed by a witch? Aren’t you afraid of punishment?” I smiled. “Being with you was already my biggest punishment.”

My mate, the supreme Alpha of the wolf pack, vows to be faithful to me for life. Yet on our anniversary night, I catch the scent of another woman on him. Later at a gathering, he holds my hand and gazes at me with tender affection. He promises that I'm the only one he'll ever cherish in this life. But moments later, I catch him outside the private room with his lover, who is wrapping herself around him. He's bragging to his friends about their thrilling hookup. It's only after the family elders whip him within an inch of his life with silver-laced whips that he finally begins to understand. When he cries out my name in his fevered delirium, something shifts. He's finally learning what it means to truly lose someone. His grandfather calls me, begging. "He's dying. Please, come see him one last time." I keep my voice calm. "That was his choice." He doesn't understand that some betrayals can never be forgiven. Not from the moment they happen.

I chase after Dean Wagner for five years while Graham Ashford chases after me for seven. When Dean marries Emily Caldwell, I finally say yes to being Graham's girlfriend. Graham is over the moon. He treats me like I'm everything to him, like he'd do whatever it takes just to make me happy. But Graham doesn't believe in marriage. Even when our daughter turns four, he still hasn't married me. He won't even let her call him "Dad". One night, I overhear him joking around with his buddies. "Your daughter's already four. You still aren't bringing your wife and kid home to meet your parents?" Graham taps his knuckles on the table and laughs. "You know why I got with Nora and had a kid with her. I just want to make Emily jealous. "Nora's easy to fool. She won't ever leave me, even if I never bring her or the kid home." He thinks he has me all figured out, but he doesn't. I turn and leave without a word, then plan to leave him for good. A man like that doesn't deserve my love. And he sure as well doesn't deserve to be my daughter's father.

“Dad, I agree to move to Haven State for the arranged marriage. Let’s do it quickly before I change my mind.” Her father, Joe Stone, replied instantly. “Good girl, I’ll have it sorted within a month at most!” Just an hour ago, Tara Stone had been in the backseat of a luxury car, her soft sighs slipping out as Leo Carter kissed her. His phone rang, and he answered in Genovian, his tone impatient. “Calling at a time like this?” The voice on the other end chuckled. “What’s up? Busy with something important? How much does she resemble Nina Lucas?” Leo absentmindedly stroked Tara’s delicate face. “About seventy percent similar. If you don’t get to the point, I’m hanging up.” “Wait, don’t! Nina’s flight lands tomorrow. She’s returning to revive her career back home. I thought I’d give you a heads-up. Nice of me, right? Your first love, your ‘one true love,’ is back. Think you’ll finally ditch the stand-in? What if she won't leave you?” Leo replied coldly, “There’s no problem money can’t solve.” Tara, her head lowered against the seat, felt her tears streaming uncontrollably. Leo had no idea she understood Genovian. Three years of heartfelt devotion, and to him, she was nothing more than a dog.

In my previous life, I married the Underboss of the Marino family to forge an alliance between our mafia families. However, he treated me with nothing but cold indifference. In the end, he conspired with his mistress and left me to burn alive. When I opened my eyes again, I was 22 years old once more. I was back at that party where he had locked me out for her sake. This time, I did not cry. I simply turned and walked away. I tore up our marriage contract myself, built my own fashion empire, and met a man who actually respected and loved me. The irony of it all? The same man who once threw me away like garbage now chased after me like a mad dog, desperate to fix what he had broken. "Rosalie, just come back with me now and I'll pretend none of this ever happened!" His eyes were bloodshot as he begged. I looked at him and laughed. What happened could not be erased just because he wanted it to be. In this lifetime, I would bask in the sunlight and live just for myself.

On our fifth dating anniversary, my boyfriend, Luke Bolton, gives me a cheap bracelet worth less than a hundred dollars. On the same night, he splurges ten million dollars on a yacht for his first love, Cindy Gale. I refuse to accept this, and he accuses me of making a scene. "I gave Cindy that gift to boost the company's stock price, not because I still have feelings for her," he says. "You're poor, and I still promised to marry you. Isn't that enough? This was actually your last test, Elisa Gray, but you failed it." I break up with him, and he immediately proposes to Cindy. Five years after that, we meet again at a luxury hotel during a business summit. His company is about to become an industry giant, and Cindy is holding onto his arm. When he sees me, I'm standing in a fountain, all drenched and disheveled. "Elisa," Luke sneers. "When you turned me down back then, did it ever cross your mind that you might end up worse than a homeless person? "Don't think acting pitiful here will make me feel sorry and take you back." I ignore him. My son's cherished blue diamond was a birthday gift from his father, and he accidentally dropped it into the fountain. He's so upset that he's about to cry, and I have to find it right away.

The Don of the Falcieri family was assassinated by a rival family, leaving behind his widowed wife, Livia. His younger brother, my husband Caius, took his place as Don. With the title came a duty: to secure the Falcieri bloodline by putting a child in his brother's widow. "Alessia's been barren for years. It falls to Livia to do what she couldn't. The Falcieri family cannot be without an heir." The Madre's voice dripped with scorn. Caius held me close, whispering promises. "As soon as Livia is pregnant, I swear I'll never touch her again." "Alessia, you're the only one I love." Three months, and he hasn't set foot in our bedroom. After he ignored me in front of everyone, choosing Livia time and time again, I finally left. I took what was mine and left one thing behind: a DNA test. It was my final gift to Caius.

Astrid was aware that her daughter, Coco, loved her father. The problem was that the father, Isaiah, did not love her, nor did he love Coco; he only ever allowed Coco to address him as uncle. After Isaiah dismissed the three chances Coco gave him, she decided she was going to leave him for good. It was only then that Isaiah changed his mind and started pleading desperately, “My dear, I want nothing more than to hear you call me your father.”

Thor and I grew up together—we were the definition of childhood sweethearts. We'd promised to attend the same university, graduate, and marry right after senior year. Everyone envied us. They said we were a perfect match, destined for a lifetime together. And I believed that too. I truly thought I'd spend the rest of my life with him. Until the final semester of our senior year in high school, when a new transfer student named Lina joined our class. At first, the two barely spoke. But as they grew familiar, their bond deepened in ways I could no longer ignore. He started staying after school to tutor her, bringing her breakfast every morning. When she was upset, he'd take her for a drive along the coast. If she craved Italian steak, he'd have fresh cuts flown in. Even during her period, he'd quietly prepare everything she needed. I was furious. I confronted him, argued with him, and even threatened to break up. The first time I said it, he thought I was joking and coaxed me out of my anger. The second time, he dismissed it as another tantrum and tried different ways to please me. The third time, he broke down—standing outside my house in the pouring rain all night, half kneeling before me, begging for forgiveness. Again and again, I tried to leave, and every time, he refused to let me go. Yet with each reconciliation, something in him shifted. He started taking me for granted, assuming I would always come back. His patience wore thin. His apologies turned perfunctory. Even when he came to make peace, there was no sincerity left in his voice. So I said it for the hundredth time, and that was the last. That was the moment I finally gave up on him.