[1.] Problem 12 (page 43).
In addition, let Ax = b denote the above system, write the
three elimination matrices
that put A into triangular form U with
Compute M = E3,2 E3,1E2,1
as well as M -1.
[2.] Consider the 3 elimination matrices of the previous exercise.
Which of the products
commute (the product AC commutes if AB = BA).
Explain, you actually do not need to compute the products to answer
this question, you can simply reason about what elimination
[3.] Problem 19 (page 44)
[4.] Problem 17 (page 54)
[5.] Problem 30 (page 56)
[6.] Problem 13 (page 67)
[7.] Problem 15 (page 67)
[8.] Let A be a 100 by 100 square matrix.
Assume that a system of equations Ax = b has a unique solution.
Is it possible that the system of equations Ax = c for some other
right-hand-side c has either no solutions or infinitely many?
Please explain your reasoning clearly (Hint: think of what happens
when you use elimination on the augmented matrix.