Linear Independence Linear Algebra

When my grandma is on her deathbed, she tells me hoarsely that her only wish is to see me get married. I keep crying to the point that I can barely utter a word. That's when my entire family turns to look at my boyfriend, Robert Fuller. Robert lets out a small sigh before wiping my tears off my face gently. Then, he leads me out of the ward. But as soon as the door is closed behind us, his expression goes cold. "Clary, we've been together for seven years. You know I hate getting forced into doing things by others the most. "Love is something that occurs by nature. It shouldn't be forced to happen just because others have opinions on how it should go." He strokes my hair comfortingly. "Let's not rush our marriage, hmm? Why don't we breach this topic again once things in my company go steady after it gets listed. What do you think? "Anyway, I have a meeting to attend at night. You should deal with your family for the time being. I'll bring you a gift when I visit you tonight." Before I can respond to Robert, he turns on his heel and leaves with his secretary, Mikayla Glenn. The moment they enter the elevator, I witness Mikayla standing on her tiptoes so that she can arrange Robert's tie for him skillfully. Robert never turns her away. After wiping my tears away, I return to the ward and take Grandma's hand with a smile. "Don't worry, Grandma. I'll get married in three days. Before I get married, I want you to do my hair for me."

My sister is diagnosed with leukemia after a medical checkup at the hospital where I work. My bone marrow is a match for her. Out of curiosity, I tell my family I'm the one who's sick. They vehemently oppose to her donating her bone marrow to me. "A bone marrow donation is risky! We can't let your sister put herself in danger." "Don't drag your sister into this just because you're sick. Everyone's life and death is fated—you have to accept your destiny." My sister also refuses to help me, brushing me off with the excuse that she's preparing to conceive. My relationship with my family is strained, so their behavior thoroughly destroys it. When I realize this, I leave the diagnosis report behind and walk out on them.

The pills I keep by my bedside have been swapped with vitamins. I almost die after getting a heart attack. After the stent surgery, I ask my husband, Evan Whitmore, to find out who did it. I just want the truth. However, he doesn't even look up and just brushes me off. "It was just a mistake. Cecilia probably grabbed the wrong bottle. She bought those vitamins for me. "Don't push this. She has asthma. She can't handle stress." I stare at him in shock, my chest tightening. I can't tell if the pain is from my healing heart or from the words he just threw at me. Cecilia Monroe is his secretary, and he always takes her side. That moment is when I realize that our five years of marriage mean nothing to him at all.

I died the night before my wedding to Christopher. But on the wedding day, a giant screen showed photos of me in bed with another man. In a fit of rage, Christopher smashed the screen and got engaged to my sister, Elizabeth. When my father informed him of my disappearance, Christopher sneered. “Disappeared? With the disgusting things she has done, she’s probably too ashamed to show her face!” My brother joined in with a scornful yell. “She hurt Liz, and now she has done such shameless things. I refuse to acknowledge such a wicked sister!” The shock and anger led to a fatal stroke, and my father died right there. Since then, I was despised by everyone in Cloud City. What they did not know was that it was the seemingly gentle Elizabeth who had brutally stabbed me to death and dumped my body in the river. Two months later, a fisherman found my body washed ashore.

The night of our mating ceremony, my destined Alpha, Alex, basically tossed a three-year temporary mate bond agreement at me. He said he only had eyes for one wolf girl, Lily, an Omega. He told me he’d wait until the day he was in charge of the pack, then he’d personally cut our mate bond. Lily would be his one and only. That was until Lily had a huge fight with him and just up and vanished. Alex, after too many nights drowning his sorrows, accidentally marked me. It seemed like he was finally starting to get that I was his real mate. He even started willingly holding me as we fell asleep. Just when I thought Alex had totally accepted me, Lily came back. To save Lily’s mom, Alex didn’t think twice about giving up his own precious life force. To make Lily happy, he publicly shamed me at the Moon Festival, even snatching the only moonstone bracelet my grandma had left me. Lily smashed the bracelet, and my heart broke right along with it. On our third bonding anniversary, Alex booked my favorite restaurant, wanting to say sorry. But what he didn't know was that I’d already broken our mate bond. I wasn't going back.

Oliver took a job with the city's top hockey team to find out who murdered his father. He did not plan to sleep with Alexander Whitman. Alexander is the famous hockey captain. He is huge, cold, and strictly closeted. Their secret one-night stand changes everything. Alexander's touch is hot, rough, and totally addictive. But Alexander is hiding a dark secret. His real name is Alexander Montgomery. He is the billionaire heir to the exact family that killed Oliver's dad. When Oliver finds out the ugly truth, he runs. But the Ice King will not let him go. "I will give you my money, my fame, my whole life," Alexander whispers, pressing his hard chest against Oliver. "But I will never give you your freedom."

Xena Xander returned to the past and found herself back in 1989. That year, she was thirty. Her husband, Julian Zane, was thirty-five. He had just become the youngest academician at the National Academy of Sciences. He was a national talent, and his future looked exceptionally promising. They had a pair of ten-year-old twins. Everyone said she was lucky. She was so lucky to have a good husband and sweet children. But the first thing she did after returning to the past was consult a lawyer and prepare two divorce agreements. She called Julian’s office. When the assistant realized it was her, the response was brief. “Xena, Professor Zane is busy. He doesn’t have time.” She went to the research institute to look for him, but the guard stopped her at the entrance. “Sorry, Professor Zane is unavailable right now.” After three days, she took the divorce agreement and went to see Julian’s first love. She placed the agreement in front of Moon Jensen and calmly said, “Please have Julian sign the divorce agreement. From now on, he and the two children belong to you.”

As Christmas drew near, my little sister claimed she’d seen Santa Claus in the house. “He had four legs, real long, like dead branches. He crawled on the floor like a dog. His mouth was full of teeth, and I saw him with my own eyes, climbing out of the chimney. His bones were making this clicking, clacking sound.” The Santa she described was nothing like the legends. My parents and I thought it was just her imagination. Until I posted about it online. A user named “NocturneNotes” insisted my sister wasn’t lying, and that the thing was dangerous. Panicked, I asked him what we should do. He gave me three rules: “On Christmas Eve, from 11:30 PM to 2:00 AM, the entire family must ‘sleep’ by the Christmas tree.” “You can’t actually fall asleep, or you’ll die in your sleep.” “No matter what you hear or feel, you absolutely cannot open your eyes or stop pretending to be asleep. Once it hits 2:00 AM, it will leave on its own.”

After being given a second chance at life, I made a deliberate choice to avoid Nevaeh Charlton entirely. When she enrolled at Brookshire University, I left the country and went to study in Hollandia instead. When she followed me there, I disappeared again—this time, chasing war zones across continents as a field reporter, always just out of her reach. Years passed. In the end, I returned home with the woman I loved, ready to marry her and begin a new life together. On the day of our wedding, Nevaeh was stopped outside the venue. Her eyes were rimmed red, and her voice was unsteady. "Why don't you love me anymore?"

One week before our marking ceremony, my Alpha Mate, Corey Black, looks me straight in the eye and says something unbelievable, "I want to have a pup with my long-time friend Willow." At first, I assume it's a terrible joke, but I see determination in his serious expression. I suppress the churning feeling in my stomach and ask him why. He sighs, his gaze gentle as if he's soothing an unreasonable child. "Willow's old Beta father is dying. His only dying wish is to see Willow have a pup. We're doing it through IVF, so it won't hurt our relationship. "Her father devoted his entire life to the pack. You wouldn't refuse to fulfill even his dying wish, would you? You wouldn't be that cruel, right?" I don't know how to respond. He speaks as if not letting my fated mate have a pup with another woman is selfish. Later, when I go to visit the gravely ill old Beta, Corey is holding Willow Lester in his arms. His hand gently strokes her hair as he lets her sob against his chest. The moment our eyes meet, pain strikes my very soul. My wolf lets out a desperate howl of anguish. I stumble away, only to receive a text from him on the day of our marking ceremony. "Honey, Willow and I are undergoing the IVF procedure. Let's postpone the ceremony for now." I stare blankly at those words, my hand unconsciously moving to my still-flat stomach. Since he wants so badly to have a pup with another woman, I will grant his wish and disappear with my pup.