My students only: If you submitted the early
homework by 5:00 Wednesday, you don't need to turn in problem
12 from section 2.7, problem 24 from section 3.1, problem 30 from section 3.2, or problems 10 or 11 from section 3.3 on Friday.
However, please make a note for the grader that you have done it.
Let G=
3
6
3
9
3
10
19
29
0
-2
-7
-8
-2
-7
-18
-31
.
Question 1:
Compute the determinant of G. (Hint: It should be much faster to use row-reduction (see Theorem 3) than cofactor expansion.)
Question 2:
Suppose b is a vector in R4 with integer entries
and x is a vector such that Gx=b. Will x have
integer entries? Why or why not? If not, can you say anything about the
denominators of the entries of x? (Hint: Look at Cramer's Rule).
Question 3:
If you wanted to find x, would it be faster to use Cramer's Rule or row reduction? Why?