Linear Independence Linear Algebra

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.

Fiery redhead Lily is known for her fierce independence and untamed spirit. But when her brother gets into deep trouble with the notorious Black Ravens, she finds herself caught in a dangerous bind. The only way to repay his debt and keep him alive is to entangle herself with the gang's arrogantly charming leader, Ryker. Ryker, with his piercing eyes and commanding presence, rules his territory with an iron fist. Arrogant and unyielding, he's used to getting what he wants-and now, he wants Lily. Forced into his world, their clashing tempers and undeniable chemistry ignite a dark romance. As Lily found herself thrust into a world of rival gangs and hidden secrets, she realizes that her fiery spirit might be the perfect match for Ryker ruthless ambition. But with danger lurking at every turn, they must decide if their passionate connection can survive the risky game they're playing.

In order to save my childhood friend, I was severely burned and became a horrifying, ugly creature. But she thought that I had stuck my nose into her business and ruined her relationship with her crush. After we got married, she mocked my face multiple times in front of others and even brought her crush back home while I was around. She hated me even on her day of death. She said that if she could return to the past, she would rather die in the fire and not have anything to do with me. When I opened my eyes again, I returned to the moment before the fire. This time, I chose to give them my blessing.

When a billionaire Victor Huxley sets his eyes on Olivia Hayes, a young artist, it’s not just her beauty that captivates him, but an undefined desire that borders on obsession. Victor is a man used to get what he wants, and from the moment he first sees Olivia, he knows she must be his, at any cost. Olivia, on the other hand, is determined to make it on her own terms, and the last thing she wants is to be tied down to a man like Victor who is ruthless, domineering, and possessive. But when Victor uses his power to force her into a contractual marriage, Olivia finds herself trapped in a world of wealth and darkness, where escape seems impossible. As Victor's dark desires unravel, Olivia becomes both a captive and his obsession. She fights for her independence, while Victor struggles with his own conflicting feelings—torn between his dark need to possess her and a growing sense of genuine love. What starts as hate evolves into a twisted form of love as Olivia slowly begins to see cracks in Victor's cold demeanor. But as their relationship grows more complicated, dangerous forces and hidden pasts threaten to tear both of them apart. Will Victor be able to let go of his control, or will his obsession consume them both? And can Olivia ever forgive the man who stole her freedom, even as he becomes the only person who can truly save her? What will happen?

Claire longs for independence, but her father's controlling nature obstructs her aspirations. Her life takes a tumultuous turn with the arrival of the Blackwoods, infamous hunters of the supernatural, in her town. In a twist of fate, she meets Nate, the youngest son of the Blackwoods, and they fall deeply in love. However, their families' conflicting interests put their relationship in peril. As tensions mount and betrayals surface, Claire must navigate her way while also dealing with a rogue werewolf who is vying for the Alpha position. Will Claire and Nate's love be enough to overcome the obstacles they face, or will they succumb to the forces pulling them apart? Find out yourself. But one thing's for sure, their journey is sure to be a wild ride, filled with plenty of twists and turns along the way

Just one week into my new job, I was wrongfully accused of cooking the books, and it cost me five years behind bars. After that, my wife found out she was pregnant. She insisted on having the baby and promised to wait for me to come home. Out of gratitude, I threw myself into work after my release. I did everything I could to give them a good life. It was until one day, I overheard a conversation between my wife and our son. “Mom, don’t let Dad come out with us. It’s embarrassing! Why did you pin Mr. Scott’s crime on him back then?! And now, the girl next door keeps making fun of me, saying my dad’s a criminal!” My wife gently pulled our son close and comforted him, saying, “I promised Mr. Scott I’d help him. Your dad’s so naive. He’ll never find out.” It turned out that my supposed happy life was nothing but lies and betrayal!

Pagkatapos ng tatlong taon naming pagdadate ni Nathan Foster, inakala kong alam ko na kung saan kami tutungo. Pero hindi siya kailanman nagpropose sa akin. At sa halip ay nagawa pa niyang malove at first sight sa aking stepsister. Naging direkta at walang tigil ang ginawa niyang panliligaw dito na hindi nagiwan ng pagdadalawang isip sa aking isipan. Pero sa pagkakataong ito, hindi na ako nagbreakdown o naghintay pa sa mga mangyayari habang umaasa na babalik pa siya gaya noon. Napagdesisyunan ko nang makipaghiwalay. Itinapon ko ang lahat ng regalo niya sa akin, pinagpunit punit ko rin ang wedding dress na lihim kong binili at noong kaniyang kaarawan, iniwan ko sa aking nakaraan ang Riverdale. Nang sasakay na ako sa aking flight, nagmessage si Nathan sa akin: “Nasaan ka na? Hinihintay ka ng lahat.” Ngumiti ako, pero na ako nagreply sa kaniya habang binoblock ko siya sa bawat platform. Wala siyang ideya na dalawang linggo na ang nakalilipas mula noong tanggapin ko ang proposal ng aking college senior na si Eustace Cooper. Nang lumapag ang eroplano sa bagong siyudad na aking titirhan, nakahanda na kami ni Eustace na simulan ang bagong yugto ng aming mga buhay nang magkasama—bilang magasawa.

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.

While attending a class reunion with my wife, we ran into her old flame—Caelum Zeth. After the gathering, Talia Grant cornered Caelum against a wall. When she found out he had fallen on hard times, she kissed him. "How much do you still owe? Be with me. I'll give you 100 thousand a month. Will that be enough?" I stood quietly at the corner of the street and snapped a photo of their heartfelt reunion before sending it to my lawyer. I also forwarded it to Talia, along with a message, "Since you two are so in love, go ahead and marry him."

It was the day of our marriage. We were supposed to meet up at the City Hall, but my fiancee stood me up. I waited for her the whole day, and the only answer I got was a picture from her assistant. My girlfriend sat astride on his lap, and her arms were wrapped around his neck while they were locked in a deep kiss. "Sorry, Mr. Terraton. Sophie insisted on comforting me. You don't mind, do you?" I demanded answers from my girlfriend, but that only made her impatient. "He donated his blood to me. Yeah, I was with him, but so what? Man up, will you?" That killed any love I had for her, and I called my soon-to-be ex-girlfriend's sister. "Hey, Sylvie. Yeah, about your proposal. So will you marry me?"