圖中 Fomula 嘅 solution(解)有邊兩款可能性❓
答案係💡
一係 trivial solution(平凡解:x=0,y=0,z=0)
一係 infinitely many solutions(無限解)
右邊000係一個特別情況,想知有幾特別?首先要知「唔特別」嘅時候係點👇🏻
1. unique solution(唯一解)
2. infinitely many solutions(無限解)
3. no solution(無解)
咁如果右邊000,又有咩咁特別呢?就係特別在「x=0,y=0,z=0」永遠都符合所有算式,平凡人都會諗到嘅平凡解。我哋繼續推理:
1️⃣若然得一個解,咁就必定係「x=0,y=0,z=0」平凡解啦~
2️⃣由於「x=0,y=0,z=0」實啱,咁就唔會無解啦~
換言之,右邊000嘅解得兩個情況:一係「x=0,y=0,z=0」一係「無限咁多個解」🚀
#M2 技巧王 幫你避開考評陷阱,教你搶分技巧;M2 輕鬆攞 Lv 5+ 喇🌟
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🎲賭Sir|高階數學考試專家
🎓19 項數學公開試.以一 Take 過考取完美戰績
DSE:Math+M1+M2【5**】
CE & AL:Math+A.Math+Pure+Applied【A】
IAL:C12+C34+F1+F2+F3+M1+M2+M3+S1+S2+S3+D1【A】
🖥最高人氣補習網紅・貼地教數別樹一格
頻道 #杜氏數學 2016 年創辦,訂閱 65,000+,多條教學影片點擊 100,000+;2018 年獲出版社邀請,撰寫暢銷書《5**數學男人嫁得過》推廣「聰明應試」理念,並鼓勵年青人堅守自信。
🧠以心理學、高效學習融入補習教育當中
從中文大學風險管理學士畢業之後,鑽研超速學習法(Ultralearning)及教育心理學,將高效學方法先行用於自己身上,無間斷學習新知識;四年後重返校園,完成中文大學數學碩士(大數據分析)課程,期間考入門薩學會(Mensa),實證超速學習法。
🏆座右銘
好多人以為自己因為對數學無興趣,所以數學低分;事實剛好相反:因為自己數學低分,所以對數學無興趣。試諗下,若然你有歌神嘅聲線,你仲會對唱歌無興趣嗎?
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#數學 #DSE #dser #math #maths #afterschool #dsemath #examskills #mathtutor #followme #2021DSE #2022DSE #2023DSE #tutor #mathtutor #DSEfighter #tutotial
trivial中文 在 翻譯這檔事 Facebook 的精選貼文
花博絮語:從不請專業口譯到官網文宣菜英文——臺中宣言
花博又「花現」問題!
(「花現GNP」是花博宣傳口號 XD)
談談臺中市府官網宣傳《臺中宣言》的英文標題,見圖。
原版:累贅、不像樣的的台式菜英文:
《Taichung Declaration》has redefined the GNP Promote and raise the proposal for Green, Nature and People
設法順著原標題想表達的意思改成及格的英文:
The Taichung Declaration has redefined the pursuit of GNP growth in a new proposal of Green, Nature, and People
英文雖然對了,但仍累贅,沒有標題的樣子。
再改,使其精簡易懂,有標題樣:
The Taichung Declaration redefines GNP as Green, Nature, and People
最後這標題比較令人滿意,簡明、有重點、有哏。
* 重點明確:臺中宣言提出GNP新定義
* 明示GNP所代表的新名,但細節賣關子
* 藉此吸引讀者閱讀內文一探究竟
原標題在文法、寫作上的問題:
* 英文不存在中文新式書名號《……》
* 亂用動詞原形raise,不合文法
* 「GNP Promote」是啥?看似想表達「GNP提升」、「提升GNP」?就算視爲一個方案名,這也是糟糕的台式英文,正如Taiwan(,) Touch Your Heart 給人的感覺,無法端上國際。
問題出在把不合文法的動詞原形 promote、touch 一路用到底,不管意思如何,這顯示英語尚在牙牙學語階段,尚無動詞變化的意識和能力。
爲何 GNP Promote 是菜英文?進一步佐證:
請上 Google 搜索 "GNP Promote" (記得加英文引號),出現百餘條結果,清一色與「臺中宣言」有關,細查其實皆出自同一則臺中政府官方英文新聞文章,即本文探討的文章標題。難道「提升GNP」這概念在全人類有英語記錄的歷史中,是臺中市府首推?當然不!更合理的推論是:
一、像樣的英文不是這樣寫。
二、不像樣的這個英文表達,在全宇宙為臺中市府獨創。
這篇文宣,判斷又是不重視翻譯專業的結果。其實,有待批評的英文書寫問題還多著,有興趣的讀者不妨一讀,親自感受一下。
正如不久前逢甲大學一位外國英語教授針對「英語列爲第二官方語言」的計畫投書賴院長,批評這做法是緣木求魚,我也認爲台灣政府各層級應該檢討是否真已準備好,有能力拿出像樣的對內、對外的英語書寫。答案好像不證自明。
以下轉錄臺中官網全文,先是介紹何謂臺中宣言,後是臺中宣言英文版。(連結見留言)
~~~~~
《Taichung Declaration》has redefined the GNP Promote and raise the proposal for Green, Nature and People
Issued by Information Bureau Date:2018-04-19
Taichung will conduct World Flora Expo in November. Green productivity proposed by the City Government was based on the Flora Expo addressed concepts of Green productivity, Nature sustainability and People with Green-ability.「Taichung Declaration」is aiming for inviting 100 cities to sign up. Taichung City Mayor, Chia-lung Lin has signed the declaration with Changwon City Mayor, Ahn Sang-soo tonight at Masan Baseball Stadium in South Korea, he also kicked off the starting game for the Taiwanese baseball pitcher, Weichung Wang, who is working currently in South Korea. It’s very meaningful to have Changwon City as the first city to sign up to the Taichung Declaration.
The theme of 2018 Taichung World Flora Expo is「Exploring GNP」 which change the old meaning of GNP as Gross National Product. Redefined GNP now means Green productivity, Nature sustainability and People with Green-ability for pursuing green productivity and facilitating the ecological eternity and embrace the nature in addition to pursuing the technological development. to make people’s living better. We wish to promote and raise the awareness of enhanced collaborations between international societies because this is the only way to connect people to help each other for sharing the goodness and prosperity for the world. (4/11*11)*Information Bureau.
~~~~~
Taichung Declaration:
《Taichung Declaration》
A New Proposal for GNP
Have you ever thought about that, sound of blooming, could be heard?
Modern people are busy in earning their livings when they are pursuing the development of economics and technologies. They’ve been too busy to see things through so they’ve forgotten to listen to the hearts, realize the nature how close they are relying on the environment.
In 2018, let’s find out the balance for ourselves, let’s listen to the whispers of the nature, let’s listen to the happy sounds of the blooming, we can feel the the value of life and how great to be alive. After all, the meaning of life is to make the world better.
2018 Taichung World Flora Expo will raise a new proposal for GNP. GNP has it’s own life and means Green, Nature and People so it is no more a neutral number of Gross National Product. GNP stands for green productivity and facilitating the ecological eternity to make people’s living better.
It’s the time to move forwards, it’s the time to look back to the past. When we move forwards to develop the smart technologies in the future, we should remember to turn to embrace the nature again to facilitate the ecological eternity. We believe the prosperity and environmental protection can exist concurrently while the technologies can live with the nature.
Green Productivity
City in green and green in the city. The economical growth traded off by the environment will no more last as we know quite well how to play the role as one of the members in the global village. By applying green technologies, reducing energy consumption and create the shared resources to construct a sustainable city with green production and green economics as the backbone.
Nature Sustainability
The mountain geography left from the ice age and the recent wetland scenes formed by the waves and tides are all the low polluted ecological environment and diverse biological systems we would like to sustain. We will never pay the price of nature to pursue the technological prosperity again. We will rebuild the tight connections between people and nature to find back the harmony and balance between people and nature.
People with Green-ability
We are anticipating people will develop their green concepts and capabilities. Such trivial things as personal thought, diet, living and action or big scope as urban construction and future development, all of them will become the group energy of Green to contribute to the international society. So-called green concepts is to implement the actions, including respect the varieties and embrace diversity. No matter in the aspects of culture, race, politics, education or religion, we will maintain the old traditions and develop the innovations to share a better future with everyone. The aesthetics of living is to live with varieties and grow with the compatibilities.
We believe,
The perfect balance among production, ecology and living can be obtained.
Listen to the nature, connect with the society and link to the world.
Collaborate and facilitate the development of international non-government organizations.
Create the new model of urban management.
Because we connect with each other,
We will share the achievements and good results.
~~~~~
trivial中文 在 柳俊江 Lauyeah Facebook 的最讚貼文
Stand up. Respect ✊
(Update: 中文繹版連結:https://www.facebook.com/329728177143445/posts/1800273350088913/)
“An open letter to Eric Kwok, and for everyone re homophobia, discrimination and bullying”
Dear Eric,
Imagine this. You are one of the contestants on a TV talent show. You are sitting in a room with other hopefuls and one of the judges walks into the room and demanded this: “Raise your hand if you are not homophobic.”
I’m very sure you will raise your hand.
You don’t have to answer me whether or not you really are homophobic. But stay with the feeling inside your mind. How do you feel?
Your feelings are most likely the same as the feelings of your contestants when you walked into a room and asked them to raise their hands to declare their sexual orientation publicly. Because in this day and age, homophobia is just as “controversial” as homosexuality, if not more.
The reason why I’m writing this open letter to you is because after reading your apology, I want to take the opportunity to address to you, and everyone out there, the need for proper etiquette regarding LGBT issues, and to address the forms of micro-aggression, bullying and discrimination the LGBT community faces everyday especially in the workplace.
I’m taking this incident seriously because from my personal experience, this is not just a one-time slip-up for you.
I remember long time ago I was so looking forward to meeting and working with you because you are, after all, Eric Kwok the great songwriter.
You were very friendly when we talked privately. Then I started to notice how once there were audiences, media or other people around and when the cameras were turned on, you would start making insinuating and demeaning gay jokes about me and in front of me. Jokes and comments even my closest friends wouldn’t dare to make in public.
At first, I didn’t really pay too much attention. I just brushed it off as juvenile and trivial. In fact, I had been so used to these jokes since growing up that I learned not to react much.
However, as time progressed and we worked on more occasions, the same thing would happen repeatedly. The teasing and the stereotypical gay jokes continued and you would make sure that the spotlight would fall on me afterwards. The jokes no longer felt light. They felt hostile, even vindictive.
In fact, it felt like bullying.
One of these incidents was well documented in tabloids back then and you can still look it up yourself on the internet.
I came to the realization that it was not just a one-time thing. I don’t know if it’s intentional or unintentional but it’s definitely a habit and a pattern.
So many questions would be in my mind every time after working with you. Why does Eric do that every time? Is he picking on me? Does he hate me? Is he homophobic? Does he think homosexuality is something funny? Does he do this to other people too? Did I do something that pissed him off? I remember I was nothing but courteous. So why do I deserve this?
I had no answers for all of these questions. All I knew was I became fearful of working with you, dreading what words would fall out of your mouth to put me in an awkwardly embarassing position. But still I tried to give you the benefit of the doubt. You’re from California you shouldn’t be homophobic. I even defended you in my head by telling myself to loosen up.
But it’s not just you. Throughout my years in the entertainment industry, I have encountered and endured so many chauvinistic “tough guys” who like to use homosexuality as a laughing stock or source of bad comedy which were all discriminating and demeaning, yet not funny.
It’s not only me. I’m sure many people of the LGBT community face this everyday in their workplace. People around them would claim their intentions were harmless but we all knew deep down that these “jokes” have the power to put people someone in an embarrassing, inferior and even threatening positions.
We kept quiet and tolerated. Sometimes we even felt obligated to laugh along just so we couldn’t afford to look “petty” or “stiff”, especially in front of people of higher authority and stature.
So Eric I want to ask you.
Why have you been so obsessed with my sexuality all these years?
Why are you so fascinated by other people’s sexuality?
Why is being gay such a huge issue to you even to this day that you had to make it the first thing you asked your contestants?
Why you also had to specifically make a post on social media about that fact you questioned people about their sexuality?
Why do you take so much pride publicly in your ability to guess who are the gay contestants even when they weren’t ready to share that information?
And most of all why do you find all this to be so funny?
To begin with one’s sexual orientation is a very personal thing which others have no right to intrude, even in the entertainment industry where you are supposed to be fine with “controversy”.
This is for you and everyone out there: using your power and authority to demand someone to declare his or her sexual orientation, especially in a work environment, is ancient, barbaric and unacceptable.
Kicking someone out of the closet is just pure evil.
The fact you did what you did, especially with your stature and on broadcast TV, is not only wrong, but also you are telling the Hong Kong audience that it’s alright to continue this form of intrusion and micro aggression that the LGBT community wants to see gone.
You’re leading a very poor example by giving Hong Kong audience the impression that being gay is still a taboo.
How are your contestants, who are boys of young age, going to offer new perspectives to the Hong Kong audience under your guidance if you perpetuate stereotyping and demonstrate to them that being gay is still an issue?
I feel sorry for any contestants who are in fact gay sitting in that room that day too. They must have been traumatized seeing the way you forced your inquisition. The impression you left them with is that the entertainment industry is still a very unfriendly place for gays. Is that what you want them to think?
But most of all, it’s the attitude, tone and manner with which you shared about this incident on social media, giving people the impression that any matter regarding sexual orientation is still something shameful and laughable, which is on top of list the thing that the LGBT community fights hard everyday to change.
When you said in your apology you “have great respect for gay people, especially their hard fight for equality” I became baffled as what you did, in the past to me or in that room to the boys, is the exact thing that makes the LGBT community’s ongoing fight for equality so difficult.
Putting people down, perpetuate stereotypes, heckling and ridiculing yet making it look OK is anything but liberal and respectful, or Californian. I don’t see any “entertainment values” that are of good taste if they are made up at the expense of other people’s struggle.
If this incident happened in America, where you grew up, you would’ve gotten yourself in such hot waters that you probably can’t get out of.
I just want you and everyone out there to know that it’s not okay. And it never was. Never will be.
Being “as liberal as it gets” is great. Having gay friends is great too. Having dinner with your gay friends is absolutely fabulous! Playing all these cards to avoid being labelled as “homophobic” is very convenient. But having class, empathy, kindness and authentic respect is a completely different territory. These don’t come automatically with backgrounds.
At this point you don’t owe me an apology. I just hope that after this incident you can really start working and living with the essences of a truly liberal and creative individual. Inspire changes and end stereotypes. Start new trends and break old patterns. Embrace and not segregate. Do the work.
I had been away from Hong Kong and the industry for a few years now. It breaks me heart that I have to write this sort of open letter when it’s already 2018. I want to make this industry a safer, nicer and more accepting place to work in when I return. I want members of the LGBT community in Hong Kong, who have been so supportive of me and my music, to also have safer and nicer working environment in their respective lives.
I don’t mind coming off as an over-reacting petty bitch with no sense of humour if my message finally comes through and everyone, including you, “gets it”. I rather have no sense of humour than a bad one.
To all the contestants of the show. If anyone ever asks you if you are gay and you are not ready to discuss, it’s OK to stand up for yourself and say this: “It’s a rude question to begin with. You have no right to get an answer from me to begin with. And it doesn’t matter. It SHOULDN’T matter. It’s 2018. I hope one day I can use my craft to inspire the world and to make this become a non-issue.”
But if you are ready to be open, you have my complete support and love.
Let’s hope that through acceptance, learning and effort, one day there will no longer be any “controversial questions”. Wouldn’t we like that Eric?
Yours truly,
Pong
#LGBT
#homophobia
#safeworkplace
#中文版稍後會有
Eric Kwok 郭偉亮
trivial中文 在 [線代] 想問一下"trivial representation"是什麼意思? - 看板Math 的推薦與評價
最近在準備細讀一輪線代
可是在線性相依和線性獨立的小節裡面看到這一個詞
不太明白該怎麼解釋他,查wiki也看的不明不白的~"~
所以想來麻煩版上的大家解釋給小弟聽一下XD
最好是能詳述這個詞的意思啦ˊˇˋ"
PO上原文
For any vectors U1,U2,...,Un,we have a1U1+a2U2+...+anUn=0
if a1=a2=...=an=0. We call this the trivial representation of 0 as
a linear combination of U1,U2,...Un.
在此先謝謝各位!!
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.126.41.157
謝謝樓上幾位大大!!感覺就是嗯....只要知道有這個詞
沒有甚麼特別重點的性質就是的東西哦ˊˇˋ"
※ 編輯: baozi0513 來自: 140.126.41.157 (04/13 22:57)
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