### Properties of vector spaces.

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)

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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.

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

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)

Find the gradient vector f at the indicated point P: f(x, y, z)=(x^2 + y^2 + z^2) ; P(17, 3, 2) : is the square root of

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)

(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

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?

Apply Stroke's theorem to evaluate the integral over C of (ydx + zdy + xdz), where C is the curve of intersection of the unit sphere x^2+y^2+z^2=1 and the plane x+y+z=0, traced anticlockwise viewed from the side of the positive x-axis

F(x,y) = x^3 + y - xy + 1 a) Are there points on the curve y = (x - 1)^2 where Gradient f is perpendicular to the curve? b) Find the absolute maximum and minimum of the function in the region 1 >= x >= 0 and y >= 0.

Let G be k-critical graph with respect to vertex-arboricity (k>=3). Prove that for each vertex v of G, the graph G-v is not (k-1)-critical with respect to vertex-arboricity.

Graph and label the vertex and the line of symmetry. See attachment.

1. Determine whether the following sets W are vector subspaces of the vector space V. a. V=R^4, A and B are two 3 X 4 matrices. W={X is an element of R^4:Ax-3Bx=0}. b. V=C', W={f is an element of C': f(x+3)=f(x)+5 c. V=P, W={f is an element of P: f'(2)=0} d. V=C', W={f is an element of C': The integral of f(x)dx fr