Evaluate the work done between point 1 and point 2 for the conservative field F. F 3D6xi+ 6уј+ 6z k; P 1(4, 3, 5), Р 2(5, 6, 7)

Q: 4.- (-1,2,1) 5- (3,1,1) yo (5,3,4) For which webes of L 14wns ( spans R'> W Sper $1,93 $his G 165/7

A: Since you have posted a multi sub part question according to guidelines I will solve first three…

Q: Let A= 00 b) Say if A is diagonalisable sur Cv H E M3x3(C) such that H-¹AH is diagonal.

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Q: Let x₁ = a +bt² +c+z₁, t=0, 1, 3,... where a,b and c constants and z, ~WN (0,0²). a) Let U₁ = x,…

A: Given, xt=a+bt2+c+zt , t=0, 1, 3, . . . where a, b and c constants and zt~WN0, σz2.

Q: E. If T:(x, y) -→ (x + 2, y), then T²:(x, y) → (_²_, _?_).

A: Given: Tx,y→x+2, y To determine: T2x,y→?,?

Q: Theorem 23. If u, v E Q then we can find integers a, b, d with d > 0 such that u = a and v = d'…

A: By Division Algorithm we know that,               Let a, b be two integers with b>0. Then there…

Q: If (0,1) ~ (-1,1) and (-1,1) ~ R. Deduce that (0,1) ~R

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Q: 人 そはっけ)ことス,ソフ ク=ム Cうk CurlF 支ド = 22 ズ 0y a2 %3D -> (-出)5+ (号-)k !! よいF (ス)+ C)+塩(の)こ2 ニ Find a…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: If A = (a, b) and B= (b, c), find: (i) (AUB) (ii) (AnB)' (ii) A'UB

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Q: Suppose you know that f:R? → R³ is a linear function, and that (1)- 5 and 2 (a) (6 points) What is ƒ…

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Q: 1. True/false: all linear functions U:M_(3x2)(F)->F^6 are isomorphisms. 2. True/False: If P and Q…

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Q: In Exercise 22, let u = PQ\ and v = PR\ , and find (a) the component forms of u and v, (b) u ∙ v,…

A: a) Answer(a): u=(-2,6,-2) and v=(3,6,-3)

Q: If A is diagonalizable through D= (P^-1) A P then the diagonal factorization of A = P D (P^-1)…

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Q: Find the projection of u = onto v = . projuv =

A: We can find the projection in two form one is in scalar form and other is vector form. here i give…

Q: Linear Algebra: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2. Is {p1,p2,p3} a…

A: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2.

Q: Determine if the given subset is a subspace of R^3

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Q: 4. If w = x²y + y²z + xz², show that дw Әх дw дw дz = (x + y + z)2.

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Q: Compute Cov(X,Y)

A: Solution: From the given information, the joint distribution is

Q: Let W(s,t) F(u(s, t), v(s, t)) where u(1,0)-4, u,(1,0) 3, u(1,0)- 5 v(1,0) 7, v.(1,0)=-3, v(1,0)--6…

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Q: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W. Show that V ∩W…

A: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W.  We have to…

Q: Show that the embedding of part (g) takes lines to "lines."

A: (h) We have to show that lines from ℝ2 maps to lines in P2. Lines in ℝ2 will be of the form ax+by=0.…

Q: Is the set S linearly independent? Yes No

A: We have to find

Q: Find the Value of ? P(a, b): a^ bv ( !a ^!b) ^ b == b Va (Vb P(a, b) ) == ? 3a (3b P(a, b) ) == ? a…

A: For any P,  P v !P = T                    P ^ !P = F Hence, a = {T, F} Again for any R,  R ^ !R = F…

Q: If u=(1,4)�=(1,4)  and v=(3,2)�=(3,2)  then proju(v)≈

A: The objective of this question is to find the projection of vector v onto vector u. The projection…

Q: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

Q: 2. Assume u = Z, and let A B = {..., -6, -4, -2,0,2, 4, 6,...} {-9, -6, -3,0, 3, 6, 9,...} {...,…

A: According to guidelines we can solve only first three subparts and rest part can be reposted…

Q: W = (x:x= X1 X2 LX3 where x3 = 5x₁ + 8x2

A:

Q: If there are no vectors in the set S = {a1; a2; a3} from R^3 who is a multiple of one of the other…

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Q: R^n×n is invertible, show that AB is similar to BA for all B ∈ R^n×n.

A:

Q: 5. For which value of x do the following vectors form a linearly dependent set in ¹ X₂ G

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Q: Let U₁, U2, U3 – be the following subspaces of Rª U₁={a, b, c, d)=R4| ²b=c; a=d=0}; U2={(a, b, c,…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: approximationto fx)=coshix using legendrepolynomials Find aquadratic least-squares approximati onto…

A: Using Legendre polynomials, We have to find a quadratic least-squares approximation f(x) = cosh(x).

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…

Q: 3) if Aza,i + a₂j + a³k , 13 = bi + bj + bk Prove that the .(A-B) -13 -(DXA) - A - (DXB) Vactors

A: We have to show Note: In the question  is given which is incorrect. It should be

Q: 7. Imagine 'gluing' together two tetrahedra with a common interior face that is removed. The…

A: We have to show that the sum of the outward pointing area vectors of the resulting polyhedron with 6…

Q: Q3)) Let (Z8, +8) and H=(0,2,4, 6} .Find the normalizer of (H, +8) in (Z8, +8).

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…