Consider the folloning scks V= { 0, t, 2,3 .... 1) s=( 1, 3, 5,7) 10) T=( 2, 4, 6,7,8) (J ,ר,ל ,2 )

Q: Let G = Z31, S = {1,5, 6, 25, 26, 30}. %3D %3D Prove that Cay(G, S') is normal.

A: It is given that

Q: Let X N (u,1) of size n. Obtain UMVUE for M.

A: We will use Lehmann-Scheffe theorem to find the uniformly minimum variance unbiased estimator for μ.

Q: 1. Find a non zero unit vecor ôî that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: Let's find non zero unit vector.

Q: Let, T: R' → R';T(x, y,z)= (x+y + z,2y + z,2y + 3z Tost uhothor the troncfCormotion T is linoer

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Q: Find diagonal matriy D is similar with A a A = [3 8-5

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Q: Prove that the four points P(2, ;1, 1), Q(1, 3, ; 2), R((2, 1, ; 3) and S(3, 2, 0) are coplanar

A: Given four points are  P(2,1,1)Q(1,3,2)R(2,1,3)S(3,2,0)

Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

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Q: langle of the edgen of a length of the bon's dingonhe ond z are Yedangahar bon, the Common Aruming…

A: Differentiate both the sides of the equation  s=x2+y2+z2  with respect to t and simplify to obtain…

Q: If y is orthogonal to both and then y is orthogonal to every w in Span{u, v} V. O True False

A: We have to solve given problem:

Q: Given the bases B={u , u2} and B'={u'1, u'z} for R2, where , U2 and u'2 = The transition mat rix…

A:

Q: Prove (t, to) = A(t)Þ(t, t,)

A: The variables of function t and to are independent variables.

Q: A plane P passes through the points P(3, –1, –4), E(2,7, –1), and G(-1,6, 1)

A: In this question, we have given three points P(3,-1,-4) E(2,7,-1) and G(-1,6,1) By using these…

Q: (a) Find the length of the projection of w onto v given that w = (4,7) and v = (1,1).

A: Given: w=4i+7j, v=i+j we know that projectionp→ of w onto v is given by p→=w.→v→v→2v→

Q: 15) o veclovs ú = Givetw and Tñ=211 deternine the projection d on 2.

A: This question can be solved using the projection formula.

Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

A:

Q: Consider a robot arm as given in the following figure

A: answer is in next step

Q: 2) What rule maps ABC onto A'B'C'? A. (x,y) → (x+4, y = 4) B. (x,y) → (x-3, y + 5) 4 (2-0)-²00) AY 5…

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Q: find the'mters ection d Exe sy,z]= [a,0,31++ 4,-2,178 [+sy,z]=[6,-12,--11]+5 [1,2,4]?

A:

Q: Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u…

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Q: Use a random number generator to generate five integers a, b, c, d, e, with –10 < a, b, c, d, e <10…

A: for Af continuous function  f whose  domain that includes the smooth curve CC with parameterization…

Q: If S is a subset of T , then u* (T) su* (S).

A:

Q: Is S = {a + b√(2) : a, b ∈ ℤ} dense in ℝ?

A:

Q: Show that if A is nonsingular and AB = O for an n × nmatrix B , then B = O .

A: We have given  matrix A is non singular and AB=0 for an n×n matrix  B. We have to prove that B=O

Q: 1) Let u = w² z³, where w = s?t, z = se-t. Find u when (s, t) = (1, –1).

A:

Q: 1. In the figure, E is the midpoint of (NS)¯and LSzZN. Which postulate justifies that APES = A MEN?…

A: Introduction: When two parallel lines are intersected by a transversal, the pair of angles formed on…

Q: Compute the dimension of V,(Tỷ – Tỷ, TẬT, – T†T,) C P³.

A: Given that X=ϕ is a topological space. We have to compute the dimensions of the following.…

Q: Show using MGF technique that if Z, - N(0,1), for i = 1,2,3,4,5 , then U = Ez - x² with 5 degrees of…

A: Using the MGF technique we have to prove that : U = ∑i=15Z2i ~ χ2 with 5 degrees of freedom, If Zi ~…

Q: Prove that if A is skew-symmetric matrir, Q = et is orthogonal.

A: c) To prove:- If A is skew-symmetric matrix , Q=eAt is orthogonal. Proof:- Ais skew-symmetric matrix…

Q: Find and when (TU – V)² In(W – UV) = In(2) at the point (T, U, V, W) = (1, 1, 2, 4).

A:

Q: if T(x,y) = (x,0) then Null(T) = span{(0,1)} Select one: True False

A:

Q: Let S={(x,y)∈N×N|(2−x)(2−y)<2(4−x−y)}.Prove that S=TS=T, where T={(1,1),(1,2),(2,1),(1,3),(3,1)}

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Q: Given the bases B = {u,u2} and B'= {u', u'2} for R?, where and u'= The transition mat rix Pg-g' from…

A: Linear transformation problem.....

Q: Let P = {(z, y, 2) E R° | az + by + cz = 0} where (a, b, c) # (0,0,0). (a) Prove that (a, b, c) ¢ P.…

A: Given that P=x,y,z∈ℝ3 : ax+by+cz=0 where a,b,c≠0,0,0 (a) The objective is to prove that a,b,c∉P Let,…

Q: If S is a subset of T, then u*(T) su* (S)

A:

Q: (a) Let r(t) = ti+tej+fk. Find ((1),4 × (?),1) - (1)a tuj

A: First we find out first derivative of r(t) with respect to 't' then find out 2nd derivative and then…

Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: Consider a unit square with four vertices in a two-dimensional Euclidean space, i.e., {(x1,x2)|x¿ €…

A: As per the question we have a unit square and we have to choose two points P,Q inside it uniformly…

Q: Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0)…

A: The given points can be plotted as A(3,0,0) B(0,0,2) C(0,6,0)

Q: Suppose u, VE Vand ||u|| < 1 and ||v|| < 1 . Prove it: V1- ||u||?/1- ||u||2 <1- (u, v)|

A: Suppose u, v∈V and u≤1 and v≤1 We have to prove that 1-u21-v2≤1-u,v Here, we have  u≤1 and v≤1 Also,…

Q: 10. Given: YX = ZX WX bisects ZYXZ Prove: AWYX AWZX W. Statements Reasons 1. 1. 2. 2. 3. 3. 4. 4.

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (−1, −1, 1), v = (−1, 1, −1)

A:

Q: 4. A region D in RN is said to be convex if and only if for every u, v E D and t e (0, 1), then tu +…

A: Given: A region D in ℝN is said to be convex if and only if for every u,v∈D and t∈0,1, tu+1-tv∈D.…

Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w. Provide example

A: Consider that x is orthogonal to v and w To check is it true that x is also orthogonal to v − w.   a…

Q: Prove that u, v, w ∈ R3     and [ u x v, v x w, w x u] = [ u, v, w]2

A:

Q: ZVYW E ZTXZ, WX YZ, and ZZ ZW. Complete the proof that AVWY ATZX. W

A: Given: ∠VYW≅∠TXZ , ∠Z≅∠W Also, WX≅YZ   1 Adding XY to both sides of (1). We can do this using…

Q: bet T be the relctiom an Axa olfined oy (Xı4) T(Ziwl iff xy=ZLW. Axa oifined oy Dine that T is an…

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Q: 『/ f メ,メ K、 be ars fo U()e) Tet Yu be the Larsest s the n bservotien an unbiesed estometor fr 6? E-…

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Q: Let W(s, t) = F(u(s, t), v(s, t)) Assume u(1, 0) = 2, us(1, 0) = −2, ut(1, 0) = 6 v(1, 0) = 3, vs(1,…

A: To find Ws and Wt

Q: Suppose that A = SS−1, where  is a diagonalmatrix with diagonal elements λ1, λ2, . . . , λn. Show…

A: