universal data

Chapter 232 Linear Equations
Cheng Nuo lay on the bed, continuing to read the "Analytic Geometry" in his arms.

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 read the entire book on 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 randomly chose a few of the after-school 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 dullness.

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 endings of their respective stories.

After the little fat man annoyed the grumpy senior Chen Mo with his speech, he ran errands and handed tea in front of the road show booth.By the way, he performed a family massage technique 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 give them a full set of massages.When I'm bored, I still want to chat with you.

What, disagree? !

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

Therefore, Fatty became a member of the Tsinghua Piano Club very honorably.

As for McGrady, the tragedy is no less tragic than that of Little Fatty.

Inexplicably found that the senior I like, oh, no, it's the senior!When the big dick senior who dressed up as Qiuyue Aili turned out to be a long-known women's clothing boss in the world, 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 cosplay club of Tsinghua University, 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 high-order equations in two variables, if you want to find all its solutions in the complex number domain, 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 system of equations, then y1 It is a root of R (f, g),... It can be seen from this that if we want to solve the system of equations, we must first find all the roots of R (f, g) = 0, and then substitute these roots into the system of equations, and then Find the value of x.”

In the advanced algebra class, Professor Liao stood on the podium and explained Chapter 3 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 Advanced Algebra Chapter 3 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 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 Chapter 3 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、求x=t^2-t+1和y=2t^2+t-3组成曲线的的直角坐标方程。

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 x2, x1, ... xn, and the homogeneous linear equations AX=0 and BX= 0, there are l and m linearly independent solution vectors respectively, 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: …………

…………

For the more than 30 mathematics students present under the podium, the three questions were far from simple in terms of difficulty.

After all, they have only just finished this chapter.Although they had done pre-class previews and tried a few exercises after class.

But the difficulty of the after-class exercises is really dwarfed by the difficulty of these questions given by Professor Liao.Not on the same level of difficulty at all.

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 three questions, Professor Liao gave everyone in the Mathematics Department 10 minutes to solve the problems.

Two 10 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?"

"Hello, 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 onto the podium with his head held high.

(End of this chapter)