For both 1 and 2, could you tell me whether or not there is a hyperplane that strictly separates the given sets A,B. If there is, find one. If there is not, prove so please. 1) A={(x,y):abs(x) + abs(y) <=1}, B={(1,1)} 2) A={(x,y):xy >= 4}, B={(x,y):x^2+y^2 <= 1} where abs = absolute value
1) Let u and v be vectors in R^n. a) Prove that llull = llvll if and only if u + v and u - v are orthogonal. b)Let (proj of u onto v) be the vector projection of u onto v. For u, v does not equal to 0, prove that (projection of u onto v - u) is orthogonal. 2) Find a basis for the space orthogonal to [1,1,0]^T in R^3.
1. Given the following 3 vectors, all of which lie in the horizontal plane, (see attachment for list of vectors), find: (a) 3A-B (b) 1) A?B 2) B?A (c) 1) A*B 2) B*A (d) (5A-6B+4C)?(B*C-A*B) *(Please see attachment for complete question and equations)
Let [a,b] be an interval in {see attachment}. Recall that the set of functions {see attachment} is a vector space over {see attachment} with addition (f+g)(x):=f(x)+g(x) and scalar multiplication a) choose [a,b]=[0,1]. Decide for each of the following subsets if it is a subspace. Justify your answer by giving a proof or a c
Which of the following are subspaces of the vector space ? Justify your answer. A vector space in R^3 such that every vector (a,b,c) has the property: a-b-c=2 A vector space in R^3 which has the form (a,b,a+b)
If U is a subspace of V then W=V-U (a vector x that belongs to W can not belong to U) W also is a subspace. (Proof or counterexample)
Let X: R^2 → R^3 be the parameterized surface give by X(s,t) = (s^2 - t^2 , s + t, s^2 + 3t) A) Determine a normal vector to this surface at the point (3, 1, 1) = X(2, -1) b) Find an equation for the plane tangent to this surface at the point (3, 1, 1).
Could you please give me some sort of a sketch or drawing of what a set S (its interior and its closure) would look like when: S= {(x,y) : -1<= y < cosx, -2# < x <= 2#} Note: <= is less than or equal to < is less than # is pi (3.14....).
What would a vector v in R4 such that: V(1,2,1,0) T V(1,0,-1,1) T V(0,2,0,-1) = <v> AND find scalars a,b,c,d such that <(1,2,1,0),(1,0,-1,1),(0,2,0,-1)> = <v> Please note: <v1,...,vk> denotes the vector subspace of Rn generated by the vectors v1,...,vk and that for scalars a1,...,an belonging to R, V(a1,...,an) =
Please see the attached file for the fully formatted problems. Find Edges & Vertices of Kn and Km,n.
Please see attached
The diagram attached shows a rectangular solid, two of whose vertices are A=(0,0,0) and G=(4,6,3). a) Find vector projections of AG onto the following vectors: AB, [0,1,0], [-1,0,0] and [0,0,1]. b) Find the point on AC that is closest to the midpoint of GH (The diagram is on page 21 and it is problem 6) (As you can see
Sketch hyperbola after finding Center, Vertex and Foci of this equation: (y+5)squared/16 - xsquared/9 =1 Please show steps needed
Sketch parabola first finding the vertex, foci and directrix for this equation y+3=1/8(x-5)squared meaning the (x-5) part of equation is squared.
The temperature of a plate at the point (x,y) is given by T(x,y) = 300+ 3x^2 -2y^2. A heat hating ant is located at the point (3,2). In which direction will the ant begin to walk? Give a unit vector in that direction.
( ∫ ^n_r means that n is on the top of the ∫ and r is on the bottom) Evaluate the given integral by first converting to polar coordinates: ∫ ^2_1 ∫ ^(square root of 2x - x^2)_0 (1/(square root of x^2 + y^2)) dy dx ∫: is the integral symbol
Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. (  ^n_r means that n is on the top of the  and r is on the bottom) Evaluate the iterated integral:  ^2_-1  ^3_1 (2 x - 7y) dy dx : denotes an integral
The set of vectors {[ 1 -1] , [ 1 -1] , [ 2 -1] } [ 2 0 ] [ -1 0] [ -1 0] from M_2(R) is: A. linearly dependent B. linearly independent C. orthogonal D. a spanning set for M_2(R) E. a basis for M_2(R)
Please see attachment. Require problems solving, also explanations etc for better understanding of vectors. VECTOR PROBLEMS (1) Let l be the line with equation v = a + t u. Show that the shortest distance from the origin to l can be written | a × u |
Given vector v with /v/ = 4 and direction angle of 45 degrees, write v in the form <a,b> a= 4cos 45 degrees= 4*.707=2.83 b= 4sin 45 degrees= 4*.707=2.83 vector v (a,b) becomes v(2.83, 2.83) compute (2*w).(u-v) where w = <-1, 0> 2(2<100)(5<60-4<45) 2*2<180*1.536<102.5 =6.144<282.5 or 6.144<-77.5degrees vector from equat
Use the normal gradient vector to write an equation of the line (or plane) tangent to the given curve (or surface) at the given point P: x^(1/3) + y^(1/3) + z^(1/3) = 1; P(1, -1, 1).
Please show me the steps Tahnk You A. write u in the form <a , b> B.Compute (2*u).v, where v=<sqrt(3) , -3>
Let u=<-2,1> v=<3,4> w=<-5,12> Use properties of the dot product. u(Dot)(v-w) or u.(v-w)
Please see the attached file for full problem description. 1. Demonstrate (check the properties) that the following function is an inner product in R^3. (Call R^3 with this inner product Moorean 3-space). Let u=(u_1,u_2,u_3) and v=(v_1,v_2,v_3). Then <u, v> = uAv^T, where A=[ 2 0 0 ]
Please see the attached file for the full problem description. 1. Find the rank of A= [1 0 2 0] [ 4 0 3 0] [ 5 0 -1 0] [ 2 -3 1 1] . Show work. Help:
(1) a. Find the (vector) equation of the plane passing through the points (1,2,-2), (-1,1,-9), (2,-2,-12). b. Find the (vector) equation of the plane containing (1,2,-1) and perpendicular to (3,-1,2). (2) Suppose a, b, c are non zero vectors. a. Explain why (a x b) x (a x c)
Find equations for the indictated geometrical objects The line through the point P=(1,1,1) and perpendicualar to the plane 4x-2y+6z=3
Let V= (x,y) in R2{y=3x+1} with addition and multiplication by a scalar defined on V by: (x,y)+ (x',y')= (x+x',y+y'-1) k(x,y)=(kx,k(y-1)+1) Given that with these definitions, V satisfies vector space axioms 1,2,3,6,8,9,and 10 determine whether or not V is a vector space by checking to see if axioms 4,5,7,are also satisfied.
Consider the following elements of the vector space P3 of all polynomials of degree less than or equal to 3. p(x)= x-1, q(x)=x+x2, r(x)= 1+x2-x3 Do these three polynomials form a basis for P3?