Omnipotent Data

The genius remembers the address of this site in a second: (Apex Chinese), the fastest update! No advertisements!" First, we can write x and y as f(x)=t^2-t+1-x=0 and g (x)=2t^2+t—the form of y=0."

"Then, (x, y) is determined by some t1..."

On the podium, Zhao Yang talked eloquently.

This question, in simple terms, is a problem of binary high-order equations.

As long as the value of the determinant of R(f, g) is calculated by matrix operation, the correct answer can be obtained.

In addition to the complicated calculations, it is not difficult for students in the mathematics department to come up with ideas.

"So, the equation that the desired curve of this question satisfies is 4x^2-4xy+y^2-23x+7y+19=0!"

Zhao Yang wrote down the result of his final calculation on the blackboard, and looked at Liao Zhixing who was standing beside him with searching and apprehensive eyes.

Liao Zhixing nodded in satisfaction, and said lightly, "Very well, the thinking and calculation results are correct."

Clap clap!

Students from the Department of Mathematics applauded spontaneously.

call--!

Zhao Yang let out a breath and patted his chest.

Finally... I didn't embarrass the mathematics department.

Thinking of this, Zhao Yang glanced triumphantly at Cheng Nuo who was sitting in the corner of the penultimate row.

But Cheng Nuo just raised his eyelids and ignored Zhao Yang.

Knowing that he was bored, Zhao Yang shrugged his shoulders, and was about to get off the stage when he was suddenly stopped by Liao Zhixing.

"Hey, student Zhao Yang, wait a minute."

Zhao Yang turned around in confusion.

Then, I saw Professor Liao pointing to the second question on the PPT, which is the longest question, and said to Zhao Yang with a smile, "Student Zhao Yang, since you are here, let's pass the second question to the students by the way." Let's talk about it."

"Uh……"

Zhao Yang was stunned for a moment, then the expression on his face changed for a while.

After being silent for four or five seconds, Zhao Yang said hesitantly, "Teacher, I haven't solved this problem yet."

What Zhao Yang said was the truth.

The difficulty level of the second question is not of the same order of magnitude as the first and third questions.

In these 20 minutes, Zhao Yang could barely finish except the first and third questions. As for the second question, Zhao Yang tried for a few minutes, but after finding no clue, he gave up decisively.

Difficulty level, at least to the level of postgraduate entrance examination.

If Zhao Yang was asked to do this problem when he was a sophomore and junior, he might be more than 80% sure that he could solve it.

But now, he is only a freshman, and he just finished the chapter of linear algebra less than half an hour ago, and even some places are not very clear. It is really difficult for Zhao Yang to ask him to do such a difficult problem.

"No?" Liao Zhixing treated the students with a strict and harsh attitude, but he also knew that Zhao Yang didn't know this subject, and it was reasonable, so he didn't criticize Zhao Yang too much.

Liao Zhixing nodded, "Indeed. This question is indeed a bit more difficult. Then you can tell everyone about the third question first, and we will return to the second question later."

Zhao Yang nodded as if he had been pardoned, picked up the chalk that had just been placed on the lecture table, and wrote the solution to the third problem on the blackboard.

"For this question, first we convert the two formulas into f(x) and g(x), that is, f(x)=..."

It has to be said that Zhao Yang does have a unique talent in mathematics.

The organization is clear, the thinking is smooth, and the whole problem-solving process is rigorous and meticulous. In the college entrance examination, Zhao Yang also got a high score of 146 points in the subject of mathematics.

If he is given a certain amount of time to grow up, he may become the most influential person in charge of the entire Tsinghua Department of Mathematics.

It's a pity...he was born in the wrong era.

…………

"Not bad." Liao Zhixing glanced at the entire problem-solving steps written by Zhao Yang on the blackboard, and nodded in satisfaction, "The problem-solving steps are very detailed, but there is nothing redundant.

If I were the marking teacher, I would definitely give you full marks. "

"However..." Zhao Yang's face just showed a gleam of joy, but Professor Liao's voice changed, "Even if you got full marks for this question, what about the second question?"

"You don't know how to answer the second question, so you get zero points for the second question." Professor Liao's tone became serious. Make a subject that you don't know."

Professor Liao started his teaching mode, "Mathematics, students. Mathematics is the most important subject in the postgraduate entrance examination, not one of them. Especially for students in your mathematics department, mathematics is a subject. It is enough to determine the outcome of your postgraduate entrance examination."

"If you don't know political problems, you can scribble them. If you don't know English, you can copy them for reading comprehension. If you don't know math problems, you can only write solutions!"

Zhao Yang, who was speechless by Liao Zhixing, stepped off the podium and returned to his seat. At the same time, I secretly felt ruthless, I must learn the subject of mathematics well!

Liao Zhixing stood on the podium, picked up the thermos cup and took a sip of the water soaked in wolfberry, feeling a warm current flowing to his spleen and kidney. He looked around the classroom with a friendly smile on his lips, "Who among you can answer the second question, come up and tell everyone."

No one answered.

There was silence in the classroom, and a needle could be heard.

The students in the mathematics department all lowered their heads, not daring to look directly into Liao Zhixing's eyes.

No, really no!

What can they do, they are also very helpless! He could only lower his head and pretend that it had nothing to do with him.

"What, is there no one?" Liao Zhixing still had a smile on his face.

"Come on, that fat classmate Li Xiurui, can you understand this question?"

Li Xiurui stood up from his seat with black hair, "Teacher, I can't."

"What about Gu Yuan?"

"Teacher, I won't either."

"You students!" Liao Zhixing shook his head helplessly, put the lid on the thermos, and his eyes fell on Cheng Nuo who was sitting in the penultimate row and always acted as a transparent person.

"Student Cheng Nuo?"

Cheng Nuo, who was thinking about what to have for dinner today, stood up from his seat in a daze when he heard that he was being called by Professor Liao.

At the same time, the eyes of the whole class also fell on Cheng Nuo.

Everyone in the mathematics department still had a lot of resentment towards Cheng Nuo, who had been in class with them for almost a week.

why? !

It's really that Cheng Nuo is too dishonest. He is obviously a student of the finance department. He didn't take the courses of the finance department properly, so he came to their math department.

If you say run over, just run over, and we won't say anything.

But it's too much for you to steal the limelight from our mathematics department every class!

The first advanced class, the first math class, was obviously the home field of their mathematics department, but Cheng Nuo stole the limelight from more than 30 of them by himself.

And yesterday, I explained a few lessons in the first quarter.

When the professor who taught Mathematical Sciences was checking everyone's preview results, Cheng Nuo was like the teacher who divided the class into several classes. He spent the time of the class's multi-class time, and directly gave the main knowledge points and key points of the entire Mathematical Mathematical Textbook to the mathematics department. Everyone talked about it.

At that time, this operation can be said to have stunned everyone in the Department of Mathematics.

The teacher who solved the problem also opened his mouth wide, and was stunned for more than ten seconds before recovering.

However, the way he looked at Cheng Nuo was no longer like looking at an ordinary student.

In today's senior substitute class, everyone in the mathematics department felt more friendly. Cheng Nuo had been sitting in the corner of the back row the whole time, acting as a transparent person.

I thought that this class would finally belong to the performance time of their mathematics department, but unexpectedly, none of Professor Liao's questions in their mathematics department could understand.

This is so embarrassing.

Want to go, but the strength is not enough.

The most tragic thing in the world is this.

Now that Professor Liao called Cheng Nuo, the meaning couldn't be more obvious. Then, they could only hope that Cheng Nuo didn't know the solution to this problem either.

"Student Cheng Nuo, have you solved this problem? If you do, please come up and share with your classmates." Professor Liao asked Cheng Nuo with a smile.

Under the gaze of more than thirty pairs of eyes, Cheng Nuo nodded.

Then he said hesitantly, "It's done."

"However, let me go up and give a lecture, so... it's not very good."

"I was not originally a student of the Department of Mathematics. It is already a great gift to sit here and receive the teachings of Professor Liao with my classmates. As for the sacred thing of going to the podium to give lectures to the students, I absolutely do not want to do it." Dare to hope."

Cheng Nuoang raised his head, awe-inspiring, with an expression of extreme reluctance, but reluctant to give up.

"So, I decided to give this precious opportunity to the students in the Department of Mathematics! I believe they are more capable of doing this than me."

Everyone in the mathematics department: "..."

I... I wipe!

God damn it is not good to do this! Why didn't you say this when you went up to give a lecture in the first senior substitute class? !

Also let's get on, it's all over, we won't do the number 13 you haven't.

If we knew how to do it, we would have gone up to pretend to be aggressive... Uh, ahem, it’s time to go up and spread the light of wisdom, how could it be your turn!

Over there, Cheng Nuo looked puzzled at the crowd who were all looking at him, scratched his head, and said with some embarrassment, "What are you all looking at me for? Although I admit that I am very good-looking, the key issue now is Answer the questions! Classmates, go up! Don't waste the chance I gave you!"

puff--!

Everyone spat out a mouthful of old blood!

This son... this son can be so shameless!

It is simply refreshing the three views of everyone in the mathematics department.

With resentful gazes, he wished to pin Cheng Nuo to the ground and rape him.

Liao Zhixing on the podium also held his forehead speechlessly, and waved his hand to Cheng Nuo, "Student Cheng Nuo, don't waste your time. Since you know how to do it, come up and tell the students."

He didn't notice it in the first two classes, and it wasn't until now that Liao Zhixing found out that this classmate Cheng Nuo seemed to be poisonous!

"This way, isn't it good?" Cheng Nuola raised her voice, her expression was tactful and reserved, as if she wanted to welcome but refused.

"That's great!" Liao Zhixing frowned, suppressing his violent temper and opening his mouth.

"Teacher, I still don't think this is good." Cheng Nuo was still shy.

"Don't talk nonsense, hurry up and tell me the topic!" Liao Zhixing's patience had reached a certain limit.

"In that case." Cheng Nuo clasped his fists at the people around him with a graceful demeanor, "Then I'd rather be respectful than obedient, and go up and give a (zhuang) topic (bi)."

Then, he bowed his hands to Liao Zhixing who was standing on the podium, "Thank you, teacher, for your success. My disciple is a commoner who works in finance, and Gou Quan lives in troubled times. He doesn't seek to be famous at Tsinghua University. The teacher does not think his disciples are despicable and condescending. , Thirdly invite disciples to sit on the podium. Disciple, you will definitely live up to the high expectations of your master!"

Liao Zhixing: "..."

Well, now he's sure.

Cheng Nuo is indeed poisonous!

Isn't it special to talk about a topic on the podium, why are you making it seem like you want to divide the world.

Cheng Nuo walked up to the podium empty-handed. Three steps turned into two steps.

Then, under the eyes of the whole class full of resentment, he narrated the topic.

"The solution to this problem is not difficult to think of. First, when A is a symmetric matrix, if X^TAX=0, then A=0. -X=(0,...,1,...,0) Substitute ^T to get aii=0, X=(0,...,1,...,1,...,0)^T to get aij=aji=0..."

Cheng Nuo tapped on the blackboard with a serious tone, "In this way, the proof process of the first question will come out. There are at least max(l, m) solutions to (AB)X=0 linearly independent vectors."

"Then, let's look at the second question. It's still very simple,..."

Cheng Nuo, who was already familiar with the lecture process, explained the topic quite smoothly.

Standing on the podium, Cheng Nuo's flowing movements gave everyone in the mathematics department the illusion that the person standing on the podium was not a student, but a real teacher.

After the second question, Cheng Nuo asked the third most difficult question.

This question was really difficult, and Cheng Nuo had to take out a draft paper and calculate for more than ten seconds before he could prove it. It can be seen from this that Professor Liao's question is quite good.

Cheng Nuo wrote down the steps to solve the problem on the blackboard casually.

"First look at the given conditions, AX=0, and BX=0 have no common non-zero solution vector, and l+m=n, then it means that R(A)+R(B)\u0026amp;lt;n, then R (A), R(B)\u0026amp;lt;n, so the homogeneous linear equations Ax=0, and Bx=0, must have non-zero solutions. And in the non-zero solutions, the basic solution system (vector group 1, vector group 2), respectively n-R(A), n-R(B) solution vectors, then..."

Three minutes later...

"So, it is very easy to prove that β and γ are the solution vectors of AX=0 and BX=0 respectively." Cheng Nuo threw the chalk tip away, patted the chalk dust on his hands, and made the final conclusion. "Everyone, don't think that this question is so long, and make him think it is so complicated. In fact, it is a very basic question. I, a student of the finance department, can do it, and you people in the mathematics department should not be so bad. Bar."

Under the stage, there was silence.

Perfect operation, show off the audience.

Everyone wanted to speak, to refute Cheng Nuo, to say how awesome they were. In the end, they found that they had nothing to refute.

Every word Cheng Nuo said made sense. There are more than 30 people in their mathematics department, but they have been suppressed and beaten by a finance student. The embarrassment is secondary, and the main thing is the psychological frustration, which has seriously affected their mentality in class.

Just then, the bell rang for the end of get out of class.

"Think about it carefully."

After Cheng Nuo left only one sentence that made everyone fall into deep thought, he walked off the podium with a serious expression, packed up his things, waved his sleeves, and drifted away like an expert.

The corridor outside the door.

Cheng Nuo patted his chest and thought to himself:

It's so exciting to run after pretending to be aggressive!