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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

### 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 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 Fields : Divergence and Curl

Calculate the divergence and curl of the vector field F(x,y,z) = 2xi + 3yj +4zk.

### 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

### 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

### Example of a quadratic model

QUADRATIC MODELING: You will need to locate data that can be modeled using a quadratic function. Keep in mind that good candidates for quadratic models have data that both increases and decreases. Once again, I encourage you to use either online or print resources, and I would also refer you to the textbook website which has

### Vectors, Basis, Row Space, Column Space and Null Space

1. Which of the following sets of vectors are bases and why are they bases for P2 A) 1-3x+2x^2, 1+x+4x^2, 1-7x B) 4+6x+x^2, -1+4x+2x^2, 5+2x-x^2 C) 1+x+x^2, x+x^2, x^2 2. In each part use the information in the table to find the dimension of the row-space, column-space and null-space of A and the null space

### Vectors and Gradients : Direction of Most Rapid Increase; Critical Points

1. Given f(x,y,z)=x^2y^3z^6, in what direction is F(x,y,z) increasing most rapidly at the point P(1,-1,1). What is the rate of increase? 2. Locate and classify the critical points of the function h(x,y) = x^2 -4x+4xy+y^2-16y.

### Parallel and Perpendicular Vectors and Work

1 Given a = 9i - 5j and b = 7i-4j, express i and j in terms of a and b 2 Given a=<4,5,-3> and b =<4,-2,2> determine whether a and b are parrallel, perpendicular, or neither. 3 Given F = 4i -2k;..... P(0,1,0) and Q(4,0,1) find the work W done by the force (F)moving a particle in a straight line from P to Q. 4 Given a

### Prove that a tree with Delta(T)=k (Delta means maximum degree) has at least k vertices of degree 1.

I don't understand how you count the degree of the vertices. (See attached file for full problem description) --- 2.- Prove that a tree with Delta(T)=k ( Delta means maximum degree) has at least k vertices of degree 1. Proof. We prove it by contradiction. Suppose that and there are s vertices of degree 1, where s<k.

### Express each vector as linear combination of basis.

Find a subset of the vectors that forms a basis for the span of the vectors; then express each vector which is not in basis as a linear combination of the basis vectors. v1= (1, 1, -1), v2= ( 1, 0, 1), v3= ( 1, -2, 5), v4= ( 5, 3, 2)

### Vector Subspaces, Gram-Schmidt and Orthogonal Basis

1) Find the closest point to y in the subspace W spanned by v1 and v2. y= v1= v2= #2) Let y, v1, and v2 be as in exercise #1. Find the distance from y to the subspace of R4 spanned by v1 and v2. #3) The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal bas

### Explain why vectors QR and RQ are not equivalent.

The "blog" has been quiet for a while, so you decide to create a math challenge. You post the following issues and then try to address them along with the people you've been interviewing. Explain why vectors QR and RQ are not equivalent. Explain in your own words when the elimination method for solving a system of equations

### Vectors and Subspaces

2 a) Find a base for the subspace W of spanned by What is the dimension of W? b) Let 1) Show that W is a subspace of 2) Find a base for W 3) Determine the dimension of W c) Let 1) Determine whether Y is a base for , the vector space of all 2 x 2 matrices. d) Find the two values of a for which the

### Vectors in the plane and the horizontal/vertical components of force : A kite string exerts a 12-lb pull (F=12) on a kite and makes a 45° angle with the horizontal.

Please find the horizontal and vertical components of F in the problem below: A kite string exerts a 12-lb pull (F=12) on a kite and makes a 45° angle with the horizontal. Find the horizontal and vertical components of F.

### Vectors

1. Find the component form of the vector representing the velocity of a boat traveling at 8 knots, or nautical miles per hour, with a bearing of N 53-degrees W. 2. A force of 703 pounds is needed to push a stalled car up a hill inclined at an angle of 16-degrees to the horizontal. Find the weight of the car. Ignore fric

### Vectors : Arc length of a space curve

Use the integration capabilities of you graphing utility to approximate the arc length of the space curve given by: vector r(t) = t i + t^3 j + 3t K from the point (1,1,3) to the point (2,8,6). Round your answer to the nearest three decimal places. I did this problem and got the answer 2.003 X 10^10. Would you please show

### Vector-valued function word problem

A baseball is hit from a height of 3 feet with an initial speed of 120 feet per second at an angle of 30 degrees above the horizon. Find the vector-valued function describing the position of the ball t seconds after it is hit. To be a home run, the ball must clear a wall 385 feet away and 6 feet tall. Determine if this is a home

### Problems Related to Vectos: Force, Motion, and Currents

Please explain in step by step detail the following: 25. A weight of 850 pounds is suspended by two cables. One cable makes an angle of 66 degrees with a vertical line, the other makes an angle of 42 degrees with a vertical line. Find the amount of force exerted by each of the cables. 24. An airplane is scheduled to reach

### Non-Equivalence of Vectors and Elimination Versus Substitution

1. Explain why vectors QR and RQ are not equivalent. 2. Explain in your own words when the elimination method for solving a system of equations is preferable to the substitution method.

### Parabolas: Concave Up or Down, Vertex and Intercepts

Given the parabola y = -(x - 6)2 - 1, determine each of the following. 7. Identify whether the parabola y = -(x - 6)2 - 1 opens up or down. 8. Identify the vertex of the parabola y = -(x - 6)2 - 1. 9. Identify the x-intercept(s) of the parabola y = -(x - 6)2 - 1. 10. Identify the y-intercept(s) of the parabola y

### Complex Inner Products and Orthonormal Sets

Let V be the vector space of all complex valued polynomials defined over the half line [0,infinity). (a) Show that <f,g> = &#8747; 0-->&#8734; f(x) ( g(x) bar) e^-x dx is a complex inner product on V g(x) bar is g(x) with a bar on it, which I believe to be the conjugate. (b) Find an orthonormal set : {f_o, f_1} in

### Vectors in spherical and cylindrical

(a) Given A = a*p_hat + b*psi_hat + c*z_hat (cylindrical unit vectors), where a, b, and c are constants. Is A a constant vector (uniform vector field)? If not, find: the divergence and curl of A (b) If A = a*r_hat + b*theta_hat + c*phi_hat in spherical coordinates, with constant coefficients. Is A a constant vector (unifor