# 线性代数作业代写linear algebra代考|Three–dimensional space

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• 数值分析
• 高等线性代数
• 矩阵论
• 优化理论
• 线性规划
• 逼近论

## 线性代数作业代写linear algebra代考|position vector of P

If $A=\left(x_{1}, y_{1}, z_{1}\right)$ and $B=\left(x_{2}, y_{2}, z_{2}\right)$ we define the symbol $\overrightarrow{A B}$ to be the column vector
$$\overrightarrow{A B}=\left[\begin{array}{c} x_{2}-x_{1} \ y_{2}-y_{1} \ z_{2}-z_{1} \end{array}\right]$$
We let $\mathbf{P}=\overrightarrow{O P}$ and call $\mathbf{P}$ the position vector of $P$.
The components of $\overrightarrow{A B}$ are the coordinates of $B$ when the axes are translated to $A$ as origin of coordinates.

We think of $\overrightarrow{A B}$ as being represented by the directed line segment from $A$ to $B$ and think of it as an arrow whose tail is at $A$ and whose head is at B. (See Figure 8.4.)

Some mathematicians think of $\overrightarrow{A B}$ as representing the translation of space which takes $A$ into $B$.

The following simple properties of $\overrightarrow{A B}$ are easily verified and correspond to how we intuitively think of directed line segments:
(i) $\overrightarrow{A B}=0 \Leftrightarrow A=B$;
(ii) $\overrightarrow{B A}=-\overrightarrow{A B}$;
(iii) $\overrightarrow{A B}+\overrightarrow{B C}=\overrightarrow{A C}$ (the triangle law);
(iv) $\overrightarrow{B C}=\overrightarrow{A C}-\overrightarrow{A B}=\mathbf{C}-\mathbf{B}$;
(v) if $X$ is a vector and $A$ a point, there is exactly one point $B$ such that $\overrightarrow{A B}=X$, namely that defined by $\mathbf{B}=\mathbf{A}+X$.

To derive properties of the distance function and the vector function ${\overrightarrow{P_{1}}}_{2}$, we need to introduce the dot product of two vectors in $\mathbb{R}^{3}$.

（i）一种乙→=0⇔一种=乙;
(二)乙一种→=−一种乙→;
㈢一种乙→+乙C→=一种C→（三角定律）；
(四)乙C→=一种C→−一种乙→=C−乙;
(v) 如果X是一个向量并且一种一点，正好有一点乙这样一种乙→=X，即定义为乙=一种+X.

# 计量经济学代写

## 在这种情况下，如何学好线性代数？如何保证线性代数能获得高分呢？

1.1 mark on book

【重点的误解】划重点不是书上粗体，更不是每个定义，线代概念这么多，很多朋友强迫症似的把每个定义整整齐齐用荧光笔标出来，然后整本书都是重点，那期末怎么复习呀。我认为需要标出的重点为

A. 不懂，或是生涩，或是不熟悉的部分。这点很重要，有的定义浅显，但证明方法很奇怪。我会将晦涩的定义，证明方法标出。在看书时，所有例题将答案遮住，自己做，卡住了就说明不熟悉这个例题的方法，也标出。

B. 老师课上总结或强调的部分。这个没啥好讲的，跟着老师走就对了

C. 你自己做题过程中，发现模糊的知识点

1.2 take note

1.3 understand the relation between definitions