Reference no: EM131244082
Question #1. Find perpendicular distance of the plane 6x + y + 2z = 18 from origin O by first finding co-ordinates of the point P on the plane such that OP is perpendicular to the given plane.
Question #2. We have an empty cardboard box of dimensions breadth = 3 m, length = 4 m, and height = 2 m. An ant and a fly are sitting at one of the 8 corners inside the box and wish to go get some food at the corner diagonally across (the farthest point in the box for them). What is the minimum distance the fly must travel before it gets to the food? How about the ant?
Question #3. Let N = 3 and M = 2N. M-th root of 1 is given by ω = -α, where α = exp[- 2Πj/N], j = √-1. Note j2 = -1. It is verified as
ωM = ω2N = (-α)2N = (-1)2N exp[-4Πj] = cos 4Π - j sin 4Π = 1.
Using this M-th root of 1, create an (M x M) square matrix R. The (a, b)-th element of R is given by
ra,b = ω(a-1)(b-1), a = 1, 2, ..., M; b = 1, 2, ..., M.
A. Write the matrix R expressing its elements in terms of α. Show at least the top 3 x 3 part and all the elements on the four corners. Is R a Hermitian matrix?
B. Consider another (M x M) square matrix S such that the (c, d)-th element of S is given by
sc,d = ω-(c-1)(d -1), c = 1, 2, ..., M; d = 1, 2, ..., M.
Let T = SR. Write elements of T. Compute determinant of T.
C. Express R-1 in terms of S. Show your work.
D. Find the rank of the matrix R and its nullity. Are all the rows of S l.i.?
E. Solve the linear system Sx = b for M = 6 and b = [1 1 1 1 1 1]t. You may define x = Ry and solve for y first.
You may find these very useful:
exp[ja] = cos a + j sin a; 1 + a + a2 + ... + aM - 1 = [1 - aM]/(1 - a).
|
Identify the top five missteps over the last decade
: Identify the top five missteps over the last decade or so that doomed Blockbuster. Be sure to consider changes in technology, competition, consumer preferences, etc. Use credible sources to support and explain.
|
|
Equivalence classes for relation
: Let X be a set and f : X → R be a real-valued function. Show that the relation givenby x ∼ y if and only if f(x) = f(y) is an equivalence relation on X.Remark: Equivalence classes for this relation are called level sets of f.
|
|
Measurements are in square meters
: You are ordering linoleum for an 16' by 15' kitchen. When you get to the store, the measurements are in square meters. How much linoleum should you order to ensure that you cover the entire floor?
|
|
Which principles of servant leadership did you implement
: Which of Greenleaf's principles of servant leadership did you implement and learn the most about through completing the servant leadership experience? Provide examples in your discussion.
|
|
Find perpendicular distance of the plane
: TG1401 Engineering Mathematics - Find perpendicular distance of the plane 6x + y + 2z = 18 from origin O by first finding co-ordinates of the point P on the plane such that OP is perpendicular to the given plane.
|
|
What percentage of legal immigrants were 34 years or younger
: What were the top five states of residence of new legal immigrants in that year and what percentage of the total immigration did they comprise?
|
|
Analyze three potential benchmarks from quality indicators
: Analyze how benchmarks and milestones are involved in managing the use of quality indicators. Analyze three potential benchmarks and milestones from quality indicators that could be used for your plan.
|
|
How do the changing technology barriers to trade
: How do changing technology and the falling barriers to trade and investment reflect the success of this company? How does the company show corporate social responsibility in terms of labor conditions, human rights, fair trade, and the environment?
|
|
Define crm and how it is evolving through use of technology
: Define CRM and how it is evolving through the use of technology, increased competition, and increased focus on customers. Provide an analysis of the Enterprise Resource Planning.
|