Omnipotent Data

Genius remembers the address of this site in a second: (vertex Chinese), the fastest update! No ads! Cheng Nuo lay on the bed, continuing to read the "Analytic Geometry".

Cheng Nuo's browsing speed was very fast.

He just got this book last night, and he just read it this afternoon.

It can be said that before this, Cheng Nuo hadn't understood it at all, and didn't even know the content of this book.

But in just half an hour, Cheng Nuo had already finished reading the entire Analytic Geometry.

The contents inside, whether it is the coordinates and vectors of the plane, or the various curves in the space, are all clear to the chest.

Cheng Nuo also randomly chose and did a few homework questions after each chapter.

Feeling... just not feeling.

It’s just that I don’t feel anything, and the topic is made.

What else could Cheng Nuo do? He is also very helpless. There is no pleasure in challenging the limit at all. After watching it, I fell into a dull mood.

However, after-school questions are only the most basic questions for consolidating knowledge points, and they are nothing.

Cheng Nuo believed that in the following in-depth study, there would definitely be more interesting and exciting topics.

Just when Cheng Nuo had just put down his "Analytic Geometry" textbook and was about to get out of bed and ask Yuan Hua to go to the cafeteria for dinner, the little fat man and Mai Di almost went back to the dormitory.

"How are you two, why did you come back so late?" Cheng Nuo got up from the bed, supported the head of the bed, and asked the two of them with great interest.

"Hey!" Little Fatty and McGrady looked at each other and let out a long sigh. "Speaking of it, it's all tears!"

Under Cheng Nuo's questioning, the two finally told the ending of their respective stories.

After the little fat man annoyed the hot-tempered senior sister Chen Mo with that sentence, he ran errands and handed tea in front of the road show booth. By the way, he performed a set of family massage skills on senior Chen Mo's shoulders.

Awei Eighteen Styles, all activities are not discounted!

Chen Mo was instantly satisfied with Fatty's massage techniques, and immediately made a decision to include Fatty in the piano club.

As for the main task, it is to serve tea and water to the seniors and sisters, and give a full set of massages by the way. When you are bored, you have to chat with me.

What, disagree? !

Hahaha! Can you disagree with this matter if you say you don't agree?

Therefore, the little fat man became a member of the Tsinghua Piano Club very honorably.

On McGrady's side, the tragedy was no less than that of Fatty.

Inexplicably found that the senior I like, oh, no, it's the senior! When the senior girl dressed as Qiuyue Ai Li turned out to be a long-known women's clothing boss in the Jianghu, Mai Di almost desperately wanted to run away.

But... in front of a lot of bigwigs in women's clothing, how could McGrady have a chance to escape.

Under the threat of the senior "Qiuyue Aili" in the name of molestation, Mai Di signed the contract of joining the club, which was humiliating and humiliating. Forced to voluntarily join the Tsinghua Club and live under the same roof as a lot of bigwigs in women's clothing.

…………

"f(x, y)=0, g(x, y)=0. For such a system of binary high-order equations, if you want to ask for all its solutions in the field of complex numbers, you can first put f(x, y), g (x, y) is regarded as a polynomial of x, let R (f, g)=(...^_^...^_^...), if (x1, y1) is a solution of the equation system, then y1 It is a root of R(f, g),... From this we can see that if we want to solve the equation system, we must first find all the roots of R(f, g)=0, and then substitute these roots into the equation system, and then Find the value of x."

In the advanced algebra class, Professor Liao stood on the podium and explained the third chapter of advanced algebra to everyone with his unique speed.

Today is Friday, and it is already the third substitute class of this week.

One class and one big chapter, Professor Liao's teaching speed is very stable!

It also makes the students of the mathematics department miserable.

They had to read late at night every day to barely keep up with Professor Liao's speed.

That feeling seemed to bring everyone back to the time before the college entrance examination, quite sour.

However, for some difficult knowledge points, they are still half-understood.

The third chapter of Advanced Algebra taught by Professor Liao today is mainly about solving problems and methods of various linear equations. Its difficulty has risen to a higher level compared to the previous two chapters.

It is not so easy for everyone in the mathematics department to understand.

Even Zhao Yang, who was in the first row, frowned the whole time while listening to Professor Liao's lecture.

"Okay." Professor Liao put the advanced textbook on the desk and opened the PPT. "That's all I want to say about the third chapter of linear equations."

"Next, let's look at a few practice questions. Let's try to do them. It's still the old rules. I'll ask my classmates to come up and explain these questions to everyone later."

On the PPT, three questions are displayed.

1. Find the rectangular coordinate equation of the curve composed of x=t^2-t+1 and y=2t^2+t-3.

2. Let A and B satisfy the n-order square matrix on the number field K, X is the n*1-order matrix formed by the unknown quantities x1, x2, ... xn, and the homogeneous linear equations AX=0 and BX= 0, there are l and m linearly independent solution vectors, where 1 is greater than or equal to 0, and m is greater than or equal to 0.

(1) Prove that (AB)X=0 has at least max(l, m) linearly independent solution vectors.

(2) If l+m is greater than n, prove that (A+B)X=0 must have a non-zero solution.

(3) If AX=0, and BX=0 have no common non-zero solution vector, and l+m=n. Prove that any vector α in K^n can be uniquely expressed as α=β+γ, where β and γ are the solution vectors of AX=0 and BX=0 respectively.

3. Finding formula: …………

…………

From the standpoint of the more than 30 students from the Department of Mathematics present below the podium, the three questions were far from simple in terms of difficulty.

After all, they have only just finished this chapter. Although they have done pre-class preview, they also tried to do a few exercises after class.

However, the difficulty of the after-school exercises and the difficulty of these questions given by Professor Liao can really be said to be insignificant. Not on a difficulty level at all.

Swish Swish Swish!

It was still a familiar scene, and everyone in the mathematics department frowned deeply, earnestly calculating on the draft paper.

In the entire classroom, except for the rustling sound of the pen tip scratching across the paper, no noise could be heard.

For the three questions, Professor Liao gave everyone in the mathematics department 20 minutes to solve the problems.

Twenty minutes later...

"Can that student come up and explain the first question for us?" Teacher Liao stood on the podium and asked everyone with a smile.

Swish!

The first question is the easiest of the three questions.

As soon as Liao Zhixing finished speaking, seven or eight hands were raised.

"Okay, just this classmate, come up and explain your solution and ideas for us. By the way, what's your name?"

"Hi teacher, my name is Zhao Yang." Zhao Yang who was sitting in the first row stood up and said politely.

"Then Zhao Yang, come up and talk about it." Professor Liao made a gesture of invitation, and stood on the side of the podium with a smile on his face.

Zhao Yang walked up to the podium with his head held high.