Linear Independence Linear Algebra

We had been married for three years, yet my husband, Richard Thornton, who suffered from touch deprivation syndrome, still refused to consummate our marriage. Every time his condition flared up, he would only press his forehead tightly against the curve of my neck. I assumed he was saving himself for his first love, the woman who had left years ago. Then, I overheard him talking to his friends. "Stop teasing her next time. It makes her tense up every time." "Got it, Richard. But if you care about Valeria so much, why won't you touch her? It's been three years. Aren't you worried she'll leave you for someone else?" Richard shook his head. "You don't understand. The longer we're together, the harder it is to control myself around her. She's so delicate. I'm terrified I'll hurt her. As long as she's mine, I wouldn't care even if she slept with someone else first." His friends burst out laughing. "Richard, you're all talk. If you could really handle her being with another man, you wouldn't keep running to the hospital. You think we don't know what you're up to?" The next day, I found Richard's medical records. Visit after visit, he kept asking the same question, "How can I be gentler in bed? I don't want to hurt the woman I love."

On the twelfth anniversary of our mating ceremony, my Alpha mate gave me a ten-million-dollar Moonlight herb. Fresh from the healing clinic after my miscarriage, I calmly dialed his number to request the severing of our mate bond. On the other end of the line, his secretary—also his childhood sweetheart—apologized through tears: "Sage, Moonlight herb is a sacred healing herb for most werewolves. I didn't know your mother died from Moonlight herb poisoning. I didn't know you despised it most. It's all my fault for making the decision myself. Please don't be angry with the Alpha." Marcus spent a long time gently comforting her, only saying to me: "If you want to sever it, then sever it. Don't regret it later." But when I really cut off the mate bond, the powerful Alpha went crazy.

Dad and my brother, Jonah Atwood, have always favored my sister, Lisa Atwood, while resenting me. At my coming-of-age ceremony, when several werewolves in the Blackwolf pack corners and harasses me, it's Rex Vaughn, the Alpha's heir, who steps in to protect me. He throws the most extravagant mate-bonding ceremony for me, right before the Moon Goddess. Overnight, I become someone every other female wolf wishes they could be! I'm seven months pregnant when I show up at Lisa's birthday party. Somehow, we're ambushed by dark magic. As always, Dad and Jonah put Lisa first. They throw everything they have into shielding and dragging her out of the enemies' barrier, leaving me trapped in the center of the spell circle, nearly consumed. In the end, it's Rex who pulls me out. Later, I wake up in Stone Cabin, only to walk right into a scene that makes my blood run cold. "You paid off an old witch from the Darkmoon pack to set up that spell circle?" Rex's eyes blaze red with fury. "She's only seven months along, and you were already trying to rip the pup out of her? "What? Were you hoping Lily and her pup would blow up and die together?" Jonah and Dad shrink back, trying to explain themselves. "Lisa's wolf is fading fast. The old witch said the only way to save her and her wolf is to sacrifice someone with the same blood immediately…" Rex snaps, "I care about Lisa more than either of you do! Why else do you think I claimed Lily as my mate? Sure, I want to save Lisa, but not by sacrificing Lily and her pup!" That is how I learn the truth. Rex didn't bond with me because he cared. He did it to save Lisa. As it turns out, he's no different from Dad and Jonah. All they ever see is Lisa, the weak-born wolf. I was never part of the picture to begin with. Since no one's ever truly cared about me, I'll walk away with my pup.

My best friend Ada felt sorry for my eight-year crush on Theo. So when our wolves recognize each other as mate, Ada simply gave me a pheromone-enhancing herb and sent me to Theo’s bed. Intoxicated by my scent, Theo claimed me like crazy. When I woke up, he coldly agreed to hold the marking ceremony. But shortly after the marking, Theo frequently visited European packs, and stayed away for five years. I raised our son Alex alone, waiting for him at the pack. But he never came come and just told me he didn’t like puppies. Until Alex's birthday party, I saw a video where someone asked him: "Theo, what's your happiest moment?" He replied carelessly: "Last week in Europe, after putting Marcus to sleep, I took Claire to the dining table in the living room." Amidst the whistles and cheers, my hands and feet turned ice cold. Claire was his ex-girlfriend, Marcus was his ex-girlfriend's son. They say he'd been living with them these five years in Europe, so it was all true. I was completely heartbroken, submitted the mate bond dissolution to the Alpha Council, and left North America with my son, erasing our pack registration.

On the night of our ninth wedding anniversary, my husband—Damian Grant, the man who ruled the mafia by day and once ruled my heart by night—did not bring me roses. He gave the bouquet that should have been mine to Serena Lane, his personal assistant. Beneath the chandelier where we once danced on our wedding night, he turned to me with that same cold charm he once used to whisper sweet nothings in my ear. “She's pregnant.” Finally, everything fell into place. “She's a picky eater. From today onward, you’ll cook three meals a day for her. And no repeats. “She’s sensitive and hates sleeping alone, so you’ll need to move your things into the guest room.” The room fell silent. I did not raise my voice, nor did I shed a single tear. I simply picked up my packed suitcase and walked to the door. The butler tried to stop me, but Damian did not even blink. “She’ll come back.” He lazily swirled the wine in his glass. “She’ll come back crying and begging within three days.” Our guests burst out laughing. They placed a million-dollar bet right in front of me. They were betting on whether I would be back before the night was over, begging Damian to let me back in like a pathetic stray dog with my tail between my legs. However, they did not know I had already received the family heirloom from my real father. I booked my flight to get far, far away from everyone I used to know. This time, I really left.

My older sister Katie said she missed me and requested I visit her. The second day at her place, the apocalyptic heatwave arrived. I fought tooth and nail in the supermarket for food and coolant—she told me I'm shameless and have no self-respect. I offered a high price in the community chat for supplies—she sneered at me and said that anything stored for so long must be disgusting, contaminated by bacteria. Yet, she threw herself into the arms of the man living across the hallway just for a bit of food. While cuddled in his arms, she watched me die in the heatwave. When I opened my eyes again, I heard her on the phone saying she missed me. Well, keep on missing me!

Despite dreaming of attending university all my life, I ended up stuck in my farming village. I married my brother-in-law and became my nephew’s stepmother. This all happened because my sister died trying to make money for my tuition fees on the day my results came out. I thought I had failed to secure a place at university and stopped thinking about higher education out of guilt. I married my brother-in-law according to my sister’s wishes. To pay for my sins, I raised my nephew and treated him like my own son. I made money and tutored him so that he could get into Northside University. In the end, I developed late-stage cancer. Before dying, I attended my nephew’s celebration, but he publicly accused me of being a homewrecker while my husband agreed that I had seduced him. They brought out my sister, dead for eighteen years, and made me apologize to her. It was then that I found out she had faked her death and used my university admission letter to finish her study. She had become a university lecturer after tricking me into taking care of her family. Outraged, I had a cerebral hemorrhage. When I woke up, I found I had gone back to the day my sister faked her death.

I'm the last of my father's bloodline, the old Alpha of the Moonlit Howl Pack. To keep me safe, Dad wanted me to mate with either Rhys, the pack's bravest, or Finn, our top warrior with insane fighting skills. They were supposed to be the next Alpha. But the only one they actually gave a damn about was that pathetic, vicious Omega, Cassidy. They even spat on pack tradition and marked her, thinking they could kick me out after Dad died! So, after Mom passed, and they asked me with disgust who I’d finally picked as my mate… I didn’t choose either of them. I turned my back and walked straight to Harris, the Alpha of the Shadow-fang Pack. The Alpha they say is eaten up by an ancient blood curse, a terrifying monster. However, on the day Harris was supposed to come for me, Liam and Seth actually stood in front of my den, begging me like whipped pups to stay.

Just a few days before my wedding, I accidentally come across a post while scrolling online. The title reads, "To the guy getting married in this city, your fiancée's already cheated on you." Curious, I click in to see the gossip, only to realize I'm the one being talked about. A deep male voice plays in the video. "I heard you're getting married?" The woman in the frame, bare-backed and trembling, chokes back a sob. "After you left, I realized you're still the one I love most. I'm done with him. Take me away, please!" The moment I hear her voice, it feels like someone punches me straight in the chest. Then I notice something on her wrist—the luxury couple's bracelet I gave her just yesterday. And in that instant, I feel like the biggest joke of all. Turns out the fool was me.

The company had just taken off when a project my wife, Lenora Peterson, was in charge of ran into trouble. To ease her mind during her pregnancy, I went overseas in her stead, spending ten perilous years abroad before finally returning home, barely alive. Instead of the joyful reunion I had imagined, she greeted me with cold detachment and thinly veiled disgust. "Why are you back?" Lenora asked. "Today is Nathan’s housewarming party," she added. "Let’s head there first—we’ll talk later." We rode in silence the entire way. When we arrived, a ten-year-old girl came dashing over and clung to Lenora affectionately. “Mommy, why did you take so long? Daddy’s been waiting for you forever!” Daddy? My eyes burned with rage—until I saw my old friend Nathan Grant stepping out to greet us with a smile. "Lily, come to Daddy. Mommy’s tired—don’t bother her now." When I met Lenora’s eyes, the guilt I saw there told me everything I needed to know. I turned away and texted my assistant, Morgan Williamson, to begin acquiring the company that, by right, had always belonged to me. He soon reported back. "Mr. Brooke, the acquisition process will be completed in three days."