Math. 225 - Quiz 3
September 17, 2009
Use both sides of the paper if necessary (1) Let A = 3 1 20 . and b = 8 2 3 7
(a) Re-write the matrix equation AX = b as a vector equation. [Hint: use the columns of A]. 1 3 (b) Given that X = 1 and X = 0 are both sol
16. Chemistry of Benzene: Electrophilic Aromatic Substitution
Based on McMurrys Organic Chemistry, Chapter 16
Substitution Reactions of Benzene and Its Derivatives
Benzene is aromatic: a cyclic conjugated
compound with 6 electrons Reactions of benzene le
Math. 225 - Quiz 5
October 15, 2009
Use both sides of the paper if necessary Compute the determinant of the following matrices 102 (a)3 7 0 1 6 2 Solution: Expand along row one: 102 70 3 7 det 3 7 0 = 1.det +2.dett = 1(14)+2(187) = 64 . 6 2 16 1 6 2 11 1
A few summation formulas
n
X
n
X
1=n
k=1
n
X
k2 =
k=1
k=
k=1
n(n + 1)(2n + 1)
6
n
X
k3 =
k=1
n(n + 1)
2
n2 (n + 1)2
4
A few summation formulas
n
X
1=n
k=1
n
X
n(n + 1)(2n + 1)
k =
6
k=1
2
n
X
k=
k=1
n
X
k=1
k3 =
n(n + 1)
2
n2 (n + 1)2
4