2. Verify that the usual length of Vector in the has the plane properties in 3 dinensional Space (N1) to LN4) of OY a norm -

Q: The set of vectors in R? with y = -3x is a real vector space

A:

Q: 1. Prove that fo r*dr + rydy = where C1 is the line segment from (0,0) to (1,0) by using…

A:

Q: Let V = R2, defined the addition by: (uz +u2) + (vị + vz)= (U1 +V1 , Uz +V2 + 1) With standard…

A:

Q: 2. Prove that fo r*dr + xydy = -+- where C2 is the line segment from (1,0) to (0, 1) by using…

A:

Q: What is the dimension of the vector space M,x3R)?

A: SOLUTION-

Q: Let L denote the intersection line between the planes 2x-y-3z=4 and 2x+y-z=2 A) Determine a…

A: Solution of the system of equation will give the equation of the line of intersection.

Q: Let W be the union of the first and third quadrants in the xy-plane. That is, let х :xy a. If u is…

A:

Q: H.W: Let V = {(x, y): x 20} with standard operation on R2. Is Va vector space?

A: A vector space is a set V that satisfies the following 8 conditions. Here two operations "+" and "."…

Q: Compute the distance d from y to the plane in R' spanned by u1 and uz.

A: We have to find the distance d from y to the plane in R^3.

Q: Find the flux of the vector fielol F from the baunelries of the given region (o). 37 2. (D): solid…

A:

Q: 6. Consider a normed vector space S = (R,|- |). Show that, for all r, y e S, |z - y| 2 | – l9|-

A:

Q: Given F(x, y, z) = -yzi + xzj – xyzk be a vector function that passes through a surface S of z + x2…

A:

Q: Let V = {(x, y): x 20) with standard operation on R2. Is V a vector space?

A: Given set is  V={(x,y):x=>0 }

Q: . Show that (x, y) = 4x1y1 – 7x2y2 for vectors x = (x1, x2) and y = (y1 y2) in R2 defines an inner…

A: Given two vectors x and y in R2. We need to show that the given function in x and y defines an inner…

Q: Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F. dr <…

A:

Q: What is the dimension of the vector space ab c S= { EM2x (R): a =b=c} de f

A:

Q: Use the definition of the divergence to show that div(c, F, + c2F;) = c, div(F,) + cz div(F,) for…

A: F1, F2 : D ➡️ R3 are differentiable vector fields and for constant c1 and c2 we have to prove that…

Q: The dimension of the vector space R' is equal to 8. Select one: O True O False

A: Since the dimension of the vector space Rn is n. Because, Rn has n-tuple elements.

Q: Show that the SPAN {1, cos t, cos 2t} is a vector space over R

A:

Q: v.(OF = (vo) - F+o(V .F (V) F+

A:

Q: Use Divergence Theorem to evaluate .(v²z²i +z²x²j+x²y²k).ds, where S is the upper part of the sphere…

A: Gauss Divergence Theorem : ∫∫SF·ndS=∫∫∫VdivF dV From ∫∫Sy2z2i+z2x2j+x2y2k·dS, F=y2z2i+z2x2j+x2y2k

Q: Consider the vector space 2 with the inner product rgk)=x+1,then %3D

A:

Q: Use the method of Lagrange multiplier to find the 3D vector lying on the intersection of hyperplanes…

A: let u=x i+y j+z k be a 3D vector lying on the intersection of hyperplanes x+y=2 and y+z=4 that has…

Q: 10. Show that V = R² with the standard scalar multiplication, but addition defined by (x, , y.) +…

A: We have to show that the set V with the addition operation x1, y1+x2, y2=x13+x233, y13+y233 and…

Q: Let V ((x,y): x 20) with standard operation on R2. Is V a vector space?

A:

Q: Use the inner product (f, 9) = | f(x)g(x) dr %3D in the vector space CU[0, 1] of continuous…

A:

Q: Show that V={(x,2020x): x in R} is a vector space

A: According to the given information, it is required to show that the given set is a vector space.

Q: Find a vector parametrization for the intersection of the plane x + y+z = 3 and the cylinder x² + z2…

A: solution given below..

Q: Let V = {(x, y): x 20} with standard operation on R². Is V a vector %3D space?

A: Our objective is to conclude V is a vector space or not.

Q: evaluate $ A. dš over the sphere R = 3 and show whether Divergence theorem holds or not. %3D

A: Calculate surface integral over R=3 or dr=0 ∮A→×ds→=∮R cos2θ,π,0×r2sinθdθdϕ,rdϕdr,rsinθdrdθ…

Q: Show that every plane through the origin in R3 may be identified with the null space of a vector in…

A: The null space of any matrix A consists of all the vectors B such that AB = 0 and B is not zero.It…

Q: Let V = {(x, y): x 20} with standard operation on R2. Is V a vector space?

A:

Q: . What is the basis and dimension of the vector space: SPAN {1, cos t, cos 2t}

A:

Q: Let V be n-dimensional vector space over c en for any n scalars ₁, ... , E F there-

A:

Q: In the inner product space R with the dot product, the orthogonal projection of the vector 1 onto…

A: We have to find the orthogonal projection of the given vector.

Q: Let V be the first quadrant in the xy-plane; that is, let 0, a. If u and v are in V, is u + v in V ?…

A:

Q: 32. In a normed vector space (V, ||) show that B,(x) = x + B,(0) = {x + y: Ilyll <r} and that B,(0)…

A: Definition : Let ( V , || . || ) be a normed vector space .For any r &gt; 0 ,  the set Br (x)={ y ∈V…

Q: What is the basis and dimension of the vector space: SPAN {1, cos t, cos 2t}

A:

Q: Use Divergence Theorem to evaluate .v²z²i +z²x²j+x²y²k).ds, where S is the upper part of the sphere…

A: To evaluate the below integral. ∫∫sy2z2i+z2x2j+x2y2kds¯

Q: Let II be a plane passing through the origin, and let n be a non-zero vector orthogonal to II. Then…

A:

Q: Let H be the set of all points in the second quadrant in the plane V=R^2. That is, H={(x,y) | x ≤ 0,…

A: Here in the question H be the set of all points in the second quadrant in the plane V=R2. That is,…

Q: In R, let S be the piece of the plane 3x + 3y + 3z = 3 that lies in the first octant, oriented…

A: Given S is the piece of the plane 3x+3y+3z=3 that lies in the first octant oriented upward. The…

Q: H, ond H2 are subuedɔr spoces of vector space, Sp (H, U Ha) - H, +H2 show that I

A: Proof :-

Q: What is the dimension of the vector space R

A: The objective is to find the dimension of the vector space R5.

Q: Let F(x, y) = (2x + y³, 2y – x4). Compute the flux oF. F.n ds of F across the circle of radius 5…

A: Given function can be written as, Region bounded by the circle of equation,

Q: Let, T:R' → R';T(x, y,z) = (x – y,2x + 3y + 2z,x+ y+2z) . verify that [T][v], = [T (v)]; for any…

A:

Q: Show that on the saddle surface z= xy the two vector fields (Vī+x² ± i+ y°, yvī+x² ±xvI+y°) are…

A: Let f(x,y,z)=xy−zf(x,y,z)=xy−z , (a,b,c)∈the saddle surface, and calculate the total derivative…

Q: 1) Verify that d/dx(fg) is a vector space over R, or explain why it is not.

A: The objective is to find whether the ddxf.g is a vector space over ℝ. Since it is known that…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.