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A quadratic model for the data (calculated using regression on your calculator). Be sure to be clear about what each of your variables represents.
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.
Find the equation of a plane through the origin and perpendicular to: x-y+z=5 and 2x+y-2z=7
Let F be the field of real numbers and let V be the set of all sequences , (a1 , a2 .....,an ,......) , ai ? F where equality, addition.
Compute the divergence and curl of v. Show that v is neither the gradient of a function nor the curl of a C2 vector field.
A certain professor has a file containing a table of student grades, where the first line of the file contains the number of students.
Let n be a positive integer. Let A be an element of the vector space Mat(n,n,F), which has dimension n2 over F.
Show that the functions (c1 + c2sin^2x + c3cos^2x) form a vector space. Find a basis for it. What is its dimension?
If g(x,y)= x-y^2, find the gradient vector (3,-1) and use it to find the tangent line to the level curve g(x,y)= 2 at the point (3,-1).
Let triangle in R^3 have sides A,B and C and let denote L denote the line segment between the midpoints of A and B.
Draw a vector diagram that includes the resultant vector if the person walked straight from Point A to Point B.
Let C^3 be equipped with the standard inner product and Let W be the subspace of C^3 that is spanned by u=(1,0,1) and u2=(1/v3, 1/v3, -1/v 3).
Suppose {v_1, v_2, v_3} is linearly independent set of vectors in R^n. Determine which of the following sets of vectors are linearly independent.
Specify the condition that p = (x,y,z) lies in the plane of p1, p2, and p3 (as an equation in x, y, and z). Recall that the equation of a plane.
What is an example of a linearly dependent set of three vectors with the property that any single vector can be removed from the set without changing the span.
A student claims that anything that can be accomplished by a translation can be accomplished by a reflection.
Two vectors are parallel provided that one is a scalar multiple of the other. Determine whether the vectors a and b are parallel, perpendicular, or neither.
The acceleration vector a (t), the initial position r0 = r (0), and the initial velocity v0 = v (0) of a particle moving in xyz- space are given.
Find the component form of the vector v that has an initial point at (1,-2,2) and a terminal point at (3,-3,0).
A 100g mass is placed at 20 degrees and a 200g mass at 120 degrees on a force table draw the vector diagram to scale using 0.2N/cm.
The equation of the plane passing through the point R(0) and parallel to both vectors N and B of part(a).
Write a plane equation for plane passing through P (1,2,3) and perpendicular to n = .
Find a vector with the following three characteristics: initial point at the origin, collinear but in the opposite direction of vector AB , length 3.
Briefly explain, which of the following are vector spaces? The set of all real symmetric 3x3 matrices.
If A and U are two subsets of a normed vector space, and U is open, show that A+U is open. Here A+U={a+u | a belongs to A and u belongs to U}.