# Solutions of Problem Set 2.1 in Introduction to linear algebra (Gilbert Strang)

This is not the formal. This is my personal collection of solutions.

ここから第5版に変わっています。海外からの閲覧が多いため主に英語です

Introduction to Linear Algebra 5th Edition (Gilbert Strang)

2.1 Vectors and Linear Equations

• row picture and column picture of `Ax = b`

### Problem Set 2.1

If you find any mistakes, please comment.

#### Row and column pictures of `Ax = b`

1
draw the planes in the row picture, and draw the vectors in the column picture. #### Matrices that act in special ways on vectors

16
90° and 180° rotation matrices.
180° rotation matrix is the same as `-I`. 17
`P: (x,y,z) -> (y,z,x)`, `Q: (y,z,x) -> (x,y,z)`
Q is inverse of P. 19
`E: (x,y,z) -> (x,y,z+x)`, `E^(-1): (x,y,z) -> (x,y,z-x)` omit 23, 24, and 25 as I cannot write MATLAB code.

#### Challenge Problems

31
Magic matrix in which all rows and columns and diagonals add to a same number. 33
If `w` is a combination of `u` and `v`, then `Aw` is the same combination of `Au` and `Av`. 