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Vector Calculus

Solving: Multidimensional Arrays and Vectors

I need the following in C++: A certain professor has a file containing a table of student grades, where the first line of the file contains the number of students and the number of scores in the table; each row of the table represents the exam scores of a given student and each column represents the scores on a given exam. Th

Multidimensional Arrays and Vectors

I need the following in C++. The output needs to be in a table format similar to the following sample: A demographic study of the metropolitan area around Dogpatch divided it into three regions (urban, suburban, and exurban) and published the following table showing the annual migration from one region to another (the number

Prove that U is a Subspace of V and is Contained in W

Please view the attached file for the full solution. What is presented below has many missing parts as the full question could not be copied properly. Let F be the field of real numbers and let V be the set of all sequences: ( a_1, a_2, ... , a_n, ... ), a_i belongs to F, where equality, addition and scalar multiplicat

Let F be the field of real numbers and let V be the set of all sequences ( a_1, a_2, ... , a_n, ... ), a_i belongs to F, where equality, addition and scalar multiplication are defined component wise. Prove that V is a vector space over F.

Let F be the field of real numbers and let V be the set of all sequences ( a_1, a_2, ... , a_n, ... ), a_i belongs to F, where equality, addition and scalar multiplication are defined component wise. Prove that V is a vector space over F. See attached file for full problem description.

Equation of plane

Find the equation of a plane through the origin and perpendicular to: x-y+z=5 and 2x+y-2z=7

Vectors in Component From

Given points A(3, -4) and B(-5, -2): 1. Express AB in component form (-2, -6) 2. Express BA in component form -2, 3. Find |AB| and |BA|

Euclidean Spaces and Subspaces

1. Let W = {(a, b ,2a - 3b, -a + 2b)} whre a and b are real numbers. (a) In what Euclidean space does this subset reside? Explain your answer. (b) Show that W is a subspace by showing that it satisfies the closure properties. (c) Show that W is a subspace by describing W as the span of a set of vectors. (d) Explain why this

Orthogonality, Orthonormal Basis and Orthogonal Complement

Please help me with 2 attached problems. In problem 6 I can imagine the space and guess which vectors are orthogonal to (1,-1,0) like (0,0,1) for example. However, I am not sure of my approach when I do it by hand. I do not know how to approach problem 12. I am doing something completely wrong and especially need help with

Vectors and Curvature

Find k(t) for y = 1/x. ^ P.S. The curvature of a curve is k = dT/ ds, where T is the unit tangent vector. ^ ^ And k(t) = T'(t)/ r'(t)

Vector Space Theorems and Matrices

2. Use Theorem 5.2.1 to determine which of the following are subspaces of M22. Thm 5.2.1: If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if the following conditions hold. (a) If u and v are vectors in W, then u + v is in W. (b) If k is any scalar and u is any vector in W,

Vector Functions : Velocity, Speed and Acceleration of a Particle

Find the velocity, acceleration, and speed of a particle with the given position function. Sketch the path of the particle and thaw the velocity and acceleration vectors for the specified value of t. 3, r(t)= <t^2 ? 1, t>, t=1 4. r(t)=<2?t, 4 sqrt t), t=1 5. r(t)=e^t i+e^-t j, t=0

Particles, Forces and Vectors

See the attached file. 5. A particle P is acted on by three forces F1, F2 and F3, where F1 = (2i - 5j)N and F2 = (4i - 4j). Given that P is in equilibrium, a. Find F3 in terms of i and j The force F3 is now removed and P moves under the action of F1 and F2 alone. b. Find to 3 s.f. the magnitude of the resultant force

Vector Spaces and Projection Mappings

Please see the attached file for the fully formatted problems. Let V be a vector space of all real continuous function on closed interval [ -1, 1]. Let Wo be a set of all odd functions in V and let We be a set of all even functions in V. (i) Show that Wo and We are subspaces and then show that V=Wo&#8853;We. (ii) Find a pro

Vector Cross Product and Arc length

1 Given a = <4, -3, -1> and b = <1, 4, 6>, find a X b. 2 Find the arc length of the curve given by x = cos 3t, y = sin 3t, z = 4t, from t = 0 to t = pi/2.

Properties of the determinant function

Please see the attached file for the fully formatted problems. 2. Verify that det(AB) = det(A) det(B) for A = 2 1 0 and B = 1 -1 3 3 4 0 7 1 2 0 0 2 5 0 1 Is det

Vectors, Work and Orthogonal Vectors

Find the small positive angle from the positive X-axis to the vector OP that corresponds to (3,3) Find the work done by the constant force 4i-2j if the point of application moves along the line segment from P(1,1) to Q(5,7) Determine m such that the two vectors 3i-9j and mi+2j are orthogonal

Vector Fields : Divergence, Scalar Curl and Gradient

1) Given a vector field P(x, y) i + Q(x, y) j in R2, its scalar curl is the k - component of the vector curl (Pi + Qj + 0k) in R3 (the i and j components of that curl are 0). In other words, the scalar curl of the vector field Pi + Qj equals &#8706;Q/&#8706;x - &#8706;P/&#8706;y. Find the scalar curl of F(x, y) = sin (xy) i +

Finding the Vertex of a Parabola : Maximum Height

An arrow is accidentally shot into the air. The formula y = - 14x2 + 56x + 18 models the arrow's height above the ground, y, in feet, x seconds after it was released. When does the arrow reach its maximum height? What is that height? keywords: quadratic equations, vertex form

Vector Spaces and Dimensions

Problem 1. Let V be a finite-dimensional complex vector space. Then V is also a vector space over real numbers R. Show that dimV ( over R) = 2*dimV(over complex C). Hint: If B={v1, v2, ..., vn} is a basis of V over C, show that B'={v1, ..., vn, iv1, ... ivn} is a basis of V over R. Problem 2. ( extend problem1) Let L be a f

Vector Spaces and Scalar Multiplication

1)Let V be the space of all functions from R to R. It was stated in the discussion session that this is a vector space over R. Prove axioms (VS1)=For all x,y, x+y=y+x (commutativity of addition), (VS3)= There exist an element in V denoted by 0 such that x+0=x for each x in V.,(VS4)= For each element x in V there exist an element

Vecor Spaces and Linear Combinations

Let V be the space of all functions from R to R. It was stated in the discussion session that this is a vector space over R Let F be a field, V a vector space over F, and v1,...,vk vectors in V. Prove that the set Span({v1, ..., vk}) is closed under scalar multiplication. 1. Label the following statements as true or false

Vertex of a Parabola

A football is thrown, by a quarterback, to a receiver 40 yards away. The formula y = -0.025x^2 + x + 5 models the football's height above the ground, y, in feet, when it is x yards from the quarterback. How many yards from the quarterback does the football reach its greatest height? What is that height? keywords : find,