# Solutions of Problem Set 2.2 in Introduction to linear algebra (Gilbert Strang)

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

Introduction to Linear Algebra 5th Edition (Gilbert Strang)

2.2 The Idea of Elimination

### Problem Set 2.2

If you find any mistakes, please comment.

#### 1-10 are about elimination on 2 by 2 systems.

1
Write down the upper triangular system.

2
Solve the triangular system.

3
Find multiplier to make the linear system upper triangular.

4
Find multiplier to make the linear system upper triangular.

5
Singular system

6
Singular system

7
Permanent or temporary elimination breakdown

8
Find cases of elimination break down.

9
Condition of `b` to have solution

10
Draw two lines to find the solution.

#### 11-20 study elimination on 3 by 3 systems.

11
A system of linear equations can't have exactly two solutions, why?

12
Solve 3 by 3 linear system.

13
Solve 3 by 3 linear system.

14
Row exchange, singular system.

15
Row exchange, missing pivot

16
2 Row exchange, break down after row exchange

17
Missing pivot cases

18
3 by 3 example that has 9 differenct coefficients but row 2 and 3 become zero in elimination.

19
Singular case.

20
Singular case when 1 row is a combination of the other 2 rows.

21
4 by 4 systems.

22
nth pivot of the previous matrix pattern.

23
Find possible original problems given a system after elimination.

24
Elimination failure cases

25
Find 3 singular cases.

26
Look for a matrix that has specific row and column sums.

27
Solve lower triangular system by usual elimination.

28, 29
Use MATLAB.

30
Find the last corner entry that makes the matrix singular.

31
Guess how elimination works.

32
100 by 100 singular matrix A with `Ax = 0`