Math 290 Homework 1

Math 290 Homework #1
Due date: Thursday, August 24

Section 1.1 (pp. 11--13)

#1, #2, #3, #4, #5, #6. You can just say "yes" or "no" for each of these.
#12, #13.
#22, #23. You shouldn't really need a graphing calculator for these, but you can use one if you want.
#55, #56.
#59(b), #60(a,c). Here, just saying "true" or "false" is not sufficient; you really need to give a reason.
#69, #70.

Section 1.2 (pp. 25--28)

#7, #8, #9, #10, #11, #12.
#25. Do this by Gaussian elimination with back-substitution. Write out every step you take in the elimination process, and explain what you are doing (e.g., "swap R₂ and R₃", "subtract 3/2 times R₃ from R₁", etc.) You can use Example 6 (pp. 20--21) as a model for what your complete answer should look like. When you're done, check your answer against the one given in the back of the book. If it isn't the same, go back and try to find where you went wrong.
#26. Do this by Gauss-Jordan elimination. Write out and explain every step, just like #25.
#27. Do this by either Gaussian elimination with back-substitution or by Gauss-Jordan elimination, as you prefer.
#42. Think hard about what this means!
#61. Before you look in the back of the book, think about how to convert this into a system of linear equations.