MATH 2568 HOMEWORK 8
Show work for credit.
1 (REQUIRED). For each of the following linear transformations T, find the standard matrix for
T ; that is, find a matrix A so that
T (~x) = A~x,
for all ~x in the domain of T.
(a) T (x, y, z) (3x + 5z, 0, y 19z,
Math 230, Fall 2012: HW 6 Solutions
Problem 1 (p.202 #4). SOLUTION. We know that
V (X1 X2 ) = E X12 X22
2
(E[X1 X2 ])
By independence,
E[X1 X2 ] = 1 2
E X12 X22 = E[X12 ]E[X22 ]
and
E X12 = V (X1 ) + 21
=
and similarly E X22 =
2
2
2
1
+ 21
+ 22 .
Prob
MATH 2568 HOMEWORK SEVEN
Show work and/or reasoning for credit.
1 (REQUIRED). Let A be the matrix
1 2
2 1
3 0
3 1
1 3
3 3
5 0 5
0 5 5
3 6 3
Believe me when I say that the rank of A is 2. Use this fact to find
(a) the dimension of the row space of A;
(b) t
Math 2568 Sample Test 2, deLaubenfels
Show work and thinking for credit. All vectors are in Rn , for some n.
1. Find a unit vector that points in the same direction as (1, 2, 0, 2, 0).
2. Get the orthogonal projection of (1, 0, 0, 1) onto the subspace spa
GRE-quantitative
Arithmetic
Kevin
2015.10.02
GRE-quantitative reasoning ARITHMETICby Kevin
GRE Test Pattern
Time
Issue 30mins
Verbal 30mins
Mode1
Mode2
AW(I+A) V Q V Q V
AW(I+A) Q V Q V Q
Verbal
20/section 170
Quantitative 20/section 170
Argument
30mins
Q
SAMPLE PROBLEMS
BUSFIN 4230
1) Suppose that call options on a stock with strike prices of $165 and $170 cost
$5.75 and $3.75 respectively and expiration is in 4 months. How can the
options be used to create a)
Math 4530: HW 6 Solutions
Problem 1 (p.217 #1). A coin which lands heads with probability p is tossed repeatedly. Assuming
independence of the tosses, find formulae for
a) the probability that exactly 5 heads appear in the first 9 tosses;
b) the probabili