[2.] 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.
[3.] 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
[4.] Problem 20 (page 44)
[5.] Problem 21 (page 44)
[6.] Problem 3 (page 53) with A(3,1) changed from -2 to -4
[7.] Problem 14 (page 54)
[8.] Problem 17 (page 54)
[9.] Problem 26 (page 55)
[10.] Problem 6 (page 66)
[11.] Problem 15 (page 67)
[12.] 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.