"First of all, we can write x and y in the form f(x)=t^2-t+1-x=0 and g(x)=2t^2+t-y=0, respectively. ”

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

On the podium, Zhao Yang talked about it.

This problem is simply a problem of binary higher-order equations.

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

In addition to the complexity of the operation, it is not difficult for mathematics students to come up with ideas or something.

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

Zhao Yang wrote down the results of his final calculations on the blackboard, and looked at Liao Zhixing who was standing on the side with an inquiring and apprehensive gaze.

Liao Zhixing nodded with satisfaction and spoke lightly, "Very good, the ideas and calculation results are correct." ”

Bang Bang Bang!

The students from the mathematics department in the audience applauded spontaneously.

Phew——!

Zhao Yang exhaled lightly and patted his chest.

Finally...... No disgrace to the math department.

Thinking like this, Zhao Yang glanced at Cheng Nuo, who was sitting in the corner of the penultimate row, with a smug gaze.

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

Zhao Yang knew that he was bored, shrugged his shoulders, and just wanted to step off the podium, but was suddenly stopped by Liao Zhixing.

"Hey, Zhao Yang, wait a minute. ”

Zhao Yang turned around and turned back in confusion.

Then, I saw Professor Liao pointing to the second and longest question on the PPT, and said to Zhao Yang with a smile, "Zhao Yang, since you have come up, let's talk about the second question for the students by the way." ”

"Uh......"

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

After being silent for four or five seconds, Zhao Yang spoke, "Teacher, I haven't made this question yet." ”

Zhao Yang is telling the truth.

The second question, the difficulty level, is not at all an order of magnitude higher than the first and third questions.

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

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

If Zhao Yang was asked to do this question in his sophomore and junior years, he might be more than eighty percent sure that he could solve him.

But now, he is only a freshman, and he has just finished the chapter on linear algebra less than half an hour ago, and he has not even figured out some of the parts very clearly. Just let him do such a difficult topic, it is really embarrassing for Zhao Yang.

"No?" Liao Zhixing treats students with a harsh and harsh attitude, but he also knows that Zhao Yang doesn't know this question, which is reasonable, so he doesn't criticize Zhao Yang too harshly.

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

Zhao Yangru was amnestied, nodded, picked up the chalk that had been placed on the lectern just now, and wrote the solution to the third question on the blackboard.

"For this problem, first of all, we will turn 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 he took the college entrance examination, Zhao Yang also got a high score of 146 points in mathematics.

If he is given a certain amount of time to grow, he may become the man of the year in charge of the entire Tsinghua Mathematics Department.

Pity...... He was born at the wrong time.

............

"Not bad. Liao Zhixing glanced at the entire solution steps written by Zhao Yang on the blackboard, and nodded with satisfaction, "The solution steps are written in detail, but there is no redundancy, if I am the marking teacher, I will definitely give you full marks." ”

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

"You can't do the second question, so you get zero points for the second question. Professor Liao's tone became serious, "In this way, even if you write the answer to the question perfectly, it is better to understand a question that you don't know." ”

Professor Liao started his teaching mode, "Mathematics, students. Mathematics is the most important subject in the postgraduate entrance examination, and there is no one. Especially for you mathematics students, mathematics is enough to determine your success or defeat in graduate school. ”

"You can't write political problems, you can't copy reading comprehension in English, and you can only write a solution to math problems!"

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

Liao Zhixing stood on the podium, picked up the thermos cup and took a sip of wolfberry soaked water, feeling a warm current flowing to his spleen and kidneys. He looked around the classroom, with this kind smile on the corner of his mouth, "Any of you who knows the second question, come up and tell you about it." ”

No one answered.

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

The students in the Department of Mathematics lowered their heads one by one, not daring to look directly into Liao Zhixing's eyes.

No, it really won't!

What can they do, they are also helpless! They can only bow their heads and pretend that they don't care about themselves.

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

"Come on, that chubby classmate Li Xiurui, will you be able to ask this question?"

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

"What about Gu Yuan?"

"Teacher, neither will I. ”

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

"Cheng Nuo?"

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

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

For Cheng Nuo, who has been in class with them for almost a week, everyone in the mathematics department is still quite resentful.

Why?!

It's really Cheng Nuo, this guy is too inauthentic, obviously a student of the Department of Finance, and he is not good to take courses in the Department of Finance, so he came to the territory of their Department of Mathematics.

You can run over here, and we won't say anything.

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

The first class of high substitution and the first class of mathematics were obviously the home of their mathematics department, but Cheng Nuo alone stole the limelight of more than 30 of them.

And yesterday, the first session solved a few lessons.

When the professor who taught Xie Ji checked the results of everyone's preview, Cheng Nuo directly wanted to count the lectures and spent many classes in the class to directly explain the main knowledge points and key points in the entire Xie Ji textbook to everyone in the Department of Mathematics.

At that time, this operation can be said to have stunned the people in the mathematics department.

The teacher who solved the few also grew his mouth, and he was stunned for more than ten seconds before he came to his senses.

However, looking at Cheng Nuo's gaze, it didn't look like an ordinary student.

Today's high substitute class, what makes everyone in the Department of Mathematics feel more friendly is that Cheng Nuo has been sitting in the corner of the back row and has been being a transparent person.

I thought that this class would finally belong to the performance time of their mathematics department, but unexpectedly, none of the questions taught by Professor Liao in their mathematics department would know.

It's even more embarrassing.

I want to, but I don't have enough strength.

There is no more tragic thing in the world than this.

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

"Cheng Nuo, have you made this question, if you do, come up and share it 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 with a hesitant face, "It's done." ”

"But let me go up and talk about it, like this...... Not so good. ”

"I am not a mathematics student in the first place, and it is a great gift to be able to sit here and receive the teachings of Professor Liao with my classmates. As for such a sacred thing as going to the podium to give a lecture to the students, I absolutely did not dare to hope for it. ”

Cheng Nuo raised his head, righteous and awe-inspiring, with an extremely reluctant expression, but he couldn't bear to cut his love.

"So, I decided to give this precious opportunity to my math classmates, who I believe are better able to do it than I do. ”

Mathematics Faculty Members: "......"

I...... I rub!

It's not very good for God to do this! Why didn't you say this when you went up to give a lecture in the first high school substitute class?!

Also let's go on, it's all like this, will we do you don't have 13 counts yet.

If we knew how to do it, we would have gone up and pretended to be ...... Uh, ahem, it's time to go up and sow the light of wisdom, where can it be your turn!

Over there, Cheng Nuo looked at the people who were all looking at him with a puzzled face, scratched his head, and said a little embarrassedly, "What do you all look at me, although I admit that I am very good-looking, but the key question now is to answer the question! Students, you go on! Don't waste the opportunity I give you!"

Poof——!

Everyone squirted out a mouthful of old blood!

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

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

looked at Cheng Nuo with resentment, eager to press 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, "Cheng Nuo, don't waste time, since you know, then come up and tell the classmates." ”

I didn't notice it in the first two classes, but only now did Liao Zhixing realize that this Cheng Nuo classmate seems to be poisonous!

"So, isn't it okay?" Cheng Nuo raised his volume, his expression was tactful and subtle, and he looked like he wanted to welcome and refuse.

"That's good!" Liao Zhixing frowned, and forced his temper to speak.

"Teacher, I still don't think that's good. Cheng Nuo is still shy.

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

"That being the case. Cheng Nuo hugged his fists towards the people around him, and his demeanor was graceful, "Then I might as well be respectful and obey my fate, and go up to talk about the topic." ”

Then, he arched his hand to Liao Zhixing, who was standing on the podium, "Thank you teacher for your success." The disciple Ben Buyi, ploughing in finance, living in troubled times, and not seeking to be heard in Tsinghua University. The teacher does not think that the disciple is despicable, and he is indecent and humiliated, and invites the disciple to the podium. Disciple, you will live up to the high expectations of your teacher!"

Liao Zhixing: "......"

Well, now he's sure.

Cheng Nuo, this guy is indeed poisonous!

Isn't it just to talk about a topic on the podium, how did you make it seem like you want to divide the world?

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

Then, under the resentful gaze of the whole class, the topic was narrated.

First of all, when A is a symmetric matrix, if X^TAX=0, then there is A=0. -X=(0，... ，1，... ,0)^T substitution yields aii=0,X=(0,... ，1，... ，1，... ,0)^T substitution yields aij=aji=0......"

Cheng Nuo knocked on the blackboard, and his tone was heavier, "In this case, the proof process of the first question will come out." (AB)X=0 solutions of linear independent vectors, with at least max(l,m). ”

Then, let's move on to the second question. It's still very short,......"

Cheng Nuo, who is already familiar with the process of speaking, explains the topic quite fluently.

Cheng Nuo, who was standing on the podium, made smooth movements, giving everyone in the Department of Mathematics an 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 question that was the most difficult in this question.

This question is indeed difficult, so Cheng Nuo had to take out the scratch paper and calculate it for more than ten seconds before proving it. From this, it can be seen that Professor Liao's question is quite level.

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

"First of all, if we look at the given conditions, AX=0, and BX=0 have no common non-zero solution vectors, and l+m=n, then 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 and vector group 2) in the non-zero solution are n-R(A) and n-R(B) solution vectors, respectively, then ......"

Three minutes later......

So, it's easy to prove that β, γ solution vectors for AX=0 and BX=0, respectively. Cheng Nuo threw the chalk head, patted the chalk ash on his hand, and made a final summary. "Don't think that this question is so long and that he is so complicated. Actually, it's a very basic question. I can do it as a finance student, and you math people shouldn't be so bad. ”

Offstage, there was silence.

Perfect operation, show the audience.

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

Cheng Nuo's words are reasonable. There are more than 30 people in their mathematics department, but they have been pressed and beaten by a finance student. Shame is still secondary, mainly the psychological frustration, which has seriously affected their mentality in class.

At this moment, the bell rang for the end of class.

"Think about it. ”

After Cheng Nuo only left a sentence that made everyone fall into contemplation, he walked off the podium with a serious expression, packed up his things, waved his sleeves, and left like a master in the world.

Corridor outside the door.

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

It's really exciting to run away after pretending!