【线性代数】MIT Linear Algebra Lecture 1: The geometry of linear equations

Author｜ Rickyの水果摊

Time ｜ 2022.8.31

Lecture 1: The geometry of linear equations

Lecture Info

1. Instructor: Prof. Gilbert Strang

2. Course Number: 18.06

3. Topics: Linear Algebra

4. Official Lecture Resource: Resource Index of Linear Algebra

Excellent Notes on GitHub

There are some classic, excellent notes from other authors on GitHub, wihch I highly recommend you to star ⭐️ and read 📖

notes-linear-algebra (A systematic notes written in Chinese)

The-Art-of-Linear-Algebra (Focus on visualization of important concept of Linear Algebra)

Video Link

Lecture 1: The geometry of linear equations (bilibili)

Lecture 1: The geometry of linear equations (YouTube)

Key Points

1. row picture

2. column picture

3. linear combination

Active Recall Questions

1. Draw the row/column pictures of this linear equation $\{\begin{array}{l}\begin{array}{r}x-2y=1\\ 3x+2y=11\end{array}\end{array}$
2. Why do we prefer column picture than row picture?（Hint: when b changes）
3. Do the combinations of column vectors fill all plane? (Do $Ax=b$ always have a solution?)

Answer

1. Here are the 2 figures of this linear equation

   1. row picture

      

   2. column picture

      

2. Suppose we have $Ax=b$, when b changes, all lines on the row picture have to change. However, as for the column picture, the only thing we need to change is vector b

3. No (We will learn the reason from the coming lectures)