Omnipotent Data

Genius remembers the site address in one second: (Vertex Chinese), the fastest update! No ads! "First, we can write x, 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.

This problem is simply a problem of a binary system of higher power 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 complexity of calculations, it is not difficult for students in the mathematics department to come up with ideas.

"So, the equation satisfied by the curve for this problem is 4x^2-4xy+y^2-23x+7y+19=0!"

Zhao Yang wrote down the results of his final calculation on the blackboard, and looked at Liao Zhixing, who was standing on the side, with a searching but worried look.

Liao Zhixing nodded in satisfaction, spit out, "Very well, the ideas and calculation results are correct."

Happiness!

The students from the Department of Mathematics applauded spontaneously.

call--!

Zhao Yang let out a breath and patted his chest.

Finally...not ashamed of the math department.

Thinking about this, Zhao Yang glanced triumphantly at Cheng Nuo who was sitting in the corner of the second-to-last row.

But Cheng Nuo just raised his eyelids and didn't respond to Zhao Yang.

Knowing that he was boring, Zhao Yang shrugged, just about to step off the stage, but was suddenly stopped by Liao Zhixing.

"Hey, 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 smiled at Zhao Yang, "Student Zhao Yang, since you are here, then by the way, give the students the second question. Tell me about it."

"Uh……"

Zhao Yang froze for a while, then the expression on his face changed for a while.

After four or five seconds of silence, Zhao Yang hesitated and said, "Teacher, I haven't figured this out yet."

What Zhao Yang said was the truth.

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

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

The difficulty level, at least to the level of postgraduate entrance examination.

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

But now, he is only a freshman, and he has just finished learning the chapter of linear algebra less than half an hour ago, and even some places have not been fully understood. Just letting him do such a difficult question really embarrassed Zhao Yang.

"No?" Liao Zhixing treats students with a harsh and harsh attitude, but he also knows that Zhao Yang does not know this topic, and it is reasonable, so he did not criticize Zhao Yang excessively.

Liao Zhixing nodded, "Indeed. This question is indeed a bit more difficult. Then you can tell you about the third question first. We will come back to the second question later."

Zhao Yang was amnesty, nodded, picked up the chalk on the desk just now, and wrote the solution to the third question on the blackboard.

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

I have to say 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 also rigorous and meticulous. When the college entrance examination, Zhao Yang also got a high score of 146 in the subject of mathematics.

If given a certain amount of time to grow up, he may become the leading figure in the entire Tsinghua Mathematics Department.

Unfortunately... he was born in the wrong time.

…………

"Not bad." Liao Zhixing glanced at the entire problem-solving steps written by Zhao Yang on the blackboard, and nodded with satisfaction. "The problem-solving steps are written in detail, but there is nothing superfluous. If I were a marking teacher, I would definitely give it to you. Full marks."

"But..." Zhao Yang just showed a touch of joy, but he saw Professor Liao's voice change, "Even if you get full marks for this question, what about the second question?"

"You won't know the second question, so you get zero points for the second question." Professor Liao's tone became serious. "Synthesized like this, no matter how perfect your answer is, it won't be as good. Get a problem that will not be solved."

Professor Liao started his preaching model, "Mathematics, classmates. Mathematics is the most important subject in the postgraduate entrance examination, not one of them. Especially for your mathematics students, the subject of mathematics, It's enough to determine the outcome of your postgraduate entrance examination."

"If you can't write political questions, you can write silly, English can't read and comprehend, and if you don't know math questions, you can only write solutions!

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

Standing on the podium, Liao Zhixing took a thermos cup and took a sip of the medlar soaked water, feeling a warm current flowing towards his spleen and kidneys. He looked around in the classroom for a week, with a cordial smile at the corner of his mouth, "Which one of you can answer the second question, come up and tell everyone."

No one answered.

There was silence in the classroom, and needles dropped.

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

No, not really!

What can they do, they are also helpless! I can only lower my head and pretend to be irrelevant.

"Why, no one?" Liao Zhixing still had a smile on his face.

"Come on, that fat classmate Li Xiurui, do you know this question?"

Li Xiurui stood up from his seat with a black line, "Teacher, I won't."

"What about Gu Yuan?"

"Teacher, neither can I."

"You students!" Liao Zhixing shook his head helplessly, covered the thermos cup, and focused on Cheng Nuo, who was sitting in the penultimate row and had been acting as a transparent person.

"Student Cheng Nuo?"

Cheng Nuo, who was thinking about what to eat for dinner tonight, heard himself being named by Professor Liao and stood up from his seat in a daze.

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

For Cheng Nuo, who had been in class with them for almost a week, everyone in the Department of Mathematics was still quite grieving.

Why? !

Cheng Nuo is really unreliable. He is obviously a student in the finance department. If he doesn't take the course of the finance department, he just came to their mathematics department.

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

But in every class you are too much to steal the limelight of our mathematics department!

The first high-substitution class, the first few minutes, was obviously the home of their mathematics department, but Cheng Nuo alone robbed them of the more than 30 people.

And yesterday, the first lesson was solved.

When the professor who taught Juji checked the results of everyone’s preview, Cheng Nuo directly explained the main knowledge points and key points of the whole textbook to the mathematics department, just like the professor in the division of classes. He spent the time of multiple classes in the class. Everyone talked again.

At that time, this operation could be described as shocking the people in the Department of Mathematics.

The teacher of Jie Ji also grew his mouth, and was stunned for more than ten seconds before he was relieved.

However, in the eyes of Cheng Nuo, it was no longer like looking at an ordinary student.

What made everyone in the mathematics department feel more friendly in today's high substitution class is that Cheng Nuo has always been sitting in the back corner, in front of a transparent person.

I thought that this class would finally belong to their mathematics department's performance time, but unexpectedly, none of the mathematics departments of Professor Liao would know how to do the questions.

This is particularly embarrassing.

Want to go, but lack of strength.

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 can only hope that Cheng Nuo doesn't know the solution to this problem.

"Student Cheng Nuo, have you done this question? If you do it, come up and share it with the students." Professor Liao asked Cheng Nuo with a smile.

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

Then his face hesitated and said, "I have done it."

"But let me go up and talk about it, so... not so good."

"I was not originally a student in the Department of Mathematics. It is a great gift to be able to sit here and receive the teachings of Professor Liao with my classmates. As for the sacred thing of going to the podium to teach the classmates, I definitely don't Dare to hope."

Cheng Nuo raised his head, righteous and awe-inspiring, with a very unwilling but reluctant expression of love.

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

Everyone in the Department of Mathematics: "..."

I... I wipe!

It’s not very good to do this for God! Why didn't you say this when you went up to talk about the topic in the first advanced class? !

Let us go on, all like this, will we do the number 13 if you haven’t.

If we can do it, the morning special will go up and pretend to be... uh, cough cough, it is up to spread the light of wisdom, how can it be your turn!

Over there, Cheng Nuo looked at everyone who was looking at him with a puzzled face, scratching his head, and said embarrassedly, "You all see what I do. Although I admit that I am quite good, the key issue now remains Answer the question! Classmates, come on! Don't waste the opportunity I give you!"

puff--!

Everyone spewed a mouthful of old blood!

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

It is simply refreshing the three views of everyone in the Department of Mathematics.

With eyes full of resentment, they wanted to press Cheng Nuo on the ground and **** him.

On the podium, Liao Zhixing also held his forehead speechlessly and waved his hand to Cheng Nuo, "Cheng Nuo, don't waste time, if you know it, come up and tell the students."

I haven't noticed the first two classes. Until now, Liao Zhixing discovered that this student Cheng Nuo seems to be poisonous!

"That's it, isn't it?" Cheng Nuo increased the volume, his expression was tactful and implicit, and he wanted to welcome or refuse.

"That's great!" Liao Zhixing brows straight, and presses down his violent temper.

"Teacher, I still think this is not good." Cheng Nuo still looked ashamed.

"Don't talk nonsense, hurry up and talk about the topic!" Liao Zhixing's patience has reached a limit.

"That's the case." Cheng Nuo clasped his fists towards the people around him, with a handsome manner, "Then I will respect my fate, and go up and talk about (zhuang) question (bi)."

Then, he bowed his hand to Liao Zhixing, who was standing on the podium, "I also thank the teacher for his accomplishment. The disciple is a commoner, who has devoted himself to finance, and his life is in troubled times, and he does not seek to reach Tsinghua. The teacher does not regard his disciple as despicable and self-defeating. , Three disciples are invited on the podium. Disciple, will certainly live up to the high expectations of the teacher!"

Liao Zhixing: "..."

Okay, now he is sure.

Cheng Nuo is indeed poisonous!

Isn’t it just about going to the podium to talk about a topic? How can you get it done like you want to divide the world.

Cheng Nuo stepped onto the podium empty-handed, three steps turned into two steps.

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

"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) ^T can be substituted into aii=0, X=(0,...,1,...,1,...,0)^T can be substituted into aij=aji=0……"

Cheng Nuo knocked on the blackboard, his tone intensified, "In this case, the proof process of the first problem will come out. (AB)X=0 linearly independent vector solutions, there are at least max(l,m)."

"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 questions quite smoothly.

Cheng Nuo, who was standing on the podium, acted like clouds and flowing water, giving everyone in the mathematics department an illusion that the person standing on the podium was not a student, but a practical teacher.

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

This question is indeed difficult, so Cheng Nuo had to take out the draft paper and calculate it for more than ten seconds before it was proved. It can be seen from this that Professor Liao’s question is quite level~www.readwn.com~ Cheng Nuo wrote down the steps to solve the problem casually on the blackboard.

"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)<n, then R(A) ), R(B)<n, so the homogeneous linear equations Ax=0, and Bx=0 must have non-zero solutions. And the basic solution system (vector group 1, vector group 2) in the non-zero solution, Respectively nR(A), nR(B) solution vectors, then..."

Three minutes later...

"So, it is easy to prove that β and γ are the solution vectors of AX=0 and BX=0, respectively." Cheng Nuo threw the chalk head and patted the chalk dust on his hand to make a final conclusion. "Don’t look at this question as long as you think it is so complicated. In fact, it is a very basic question. I can do it as a student in the Department of Finance, and people in the Department of Mathematics should not be so bad. Right."

There was silence in the audience.

Perfect operation, the show turned 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.

What Cheng Nuo said was reasonable. They are more than 30 people in the math department, but they have been beaten by a finance student. The shame is secondary, mainly the psychological frustration, which has severely affected their mentality in class.

It just so happened that the bell rang after class.

"You guys think about it."

Cheng Nuo left only one such sentence that made everyone fall into contemplation, and then walked off the podium with a serious look, packed his things, waved his sleeves, and departed like an expert in the world.

The corridor outside the door.

Cheng Nuo patted his chest, and said in his heart:

It's so exciting to run after loading it!