Does S={(1,0,1),(2,1,0),(3,,1,1),(1,1,1)} spans R³ ? Select one: O True O False

Q: Show that the subset of R2 given by {(x, y) E R² : xy 1, x > 0} is closed.

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Q: a u, (00) = Utt , и (0, t) — 0, и (т, t) — 0, (t>0) и (х, 0) %3D0, (0<x<n, и, (х, 0) %3 * (т—г),…

A: We need to find the solution to the threshold problem in the next wave equation by the variable…

Q: Exercise 2. Show that if B + Ø then dom(A × B) = A. %3D

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Q: Express the following: as a linear combination of u = (2, 1, 4), v = (1, -1, 6) and w = (2, 2, 8).…

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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: Let E={(r,0,z) : os es T, OS zs 1, 5Vzs rs 5. Compute

A: Introduction: The triple integral ∫∫∫Ef(x,y,z)dV with the region E=(x,y,z):a≤x≤b, c≤y≤d, e≤z≤f can…

Q: Show that the subset of R2 given by {(x, y) E R² : xy = 1, x > 0} is closed.

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Q: Prove VZEC, V2|z|>|Re z| +|Im z| + |Im z| Vze C,

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Q: Let u = (1, 2, 3), v = (2, 2, −1), and w = (4, 0, −4).Find u − v + 2w.

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Q: Prove (t, to) = A(t)Þ(t, t,)

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

Q: Prove by mathematical induction: X n (U-, Y) = U=1(X nY), for V n E Z* – {1} and sets X,Y,,Y2,. Yp-…

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Q: B = { t,f,-3 is compact. IS %3D

A: See the attachment

Q: calculate the linear combinations. u = (4, 2, −6), v = (2, −1, 3)

A: Let w=(x,y,z)w=k1v1+k2v2x=k1×u+k2×2              .....,(1)y=k1×2+k2×(-1)…

Q: Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points…

A: Given:X≡4,4Y≡-12,-4Z≡-6,9The epicenter of an earthquake is determined to be 5 units from X​, 13…

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: Let u= (-1, 1), v=(-3, 4), and W= (o, - 2). Find u - v + 4w

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Q: In cach part, let T: R → R be multiplication by A, and let u = (0,1, 1) and u2 = (3, –1, 1) and uz =…

A: The solution are next step is

Q: 3. If U and V are such that u; ='x; – A, v; =y, - B, then Cov (U, V) is :

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

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Q: let (X, Z) %3. üit piece wise comnected ?

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Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

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Q: Let r, y EN such that y # 0, then y+r#0.

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Q: Show that R³ is spanned by S = {(1,1,1), (1, –1, 0), (0, 1, – 1)}.

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Q: i. Determine whether the set is linearly dependent or linearly independent. S = {(-2,1,3), (2,9,…

A: Note :- Due to our guidelines, we can solve only one question plzzz reupload rest of question and…

Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

Q: 14) 14 12

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Q: Show that R³ is spanned by S = {(1,1,1), (1, – 1, 0), (0, 1, – 1)}.

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

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Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

Q: Consider the DFA M = ({q0, q1, q2, 93}, {0, 1}, 8, go, {41, q2}), where d is defined as follows.…

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Q: Let C ~ Cauchy(0,1). Show that C² + C-2 =9 4C² + 2.

A: c^2+1/c^2 &gt;2 thats why it is equal to 4c^2+2

Q: In R4, let S = span{(1, 1, 1, 1)T ,(1, 2, 1, 3)T }. Find S⊥.

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Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: 2 Given u -1 and U , for which w is the set {u, v, w} linearly independent?

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Q: Compute u + v, 2u – v, 3u – 2v, and 0 – 3v if (a) u =| 2 3 2 (b) u= = -3 (c) u = 1 4

A: (a) Consider the given matrices, u=123 and v=201 now, use the matrices addition property,…

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: 2. Let W = Span {u1, u2, uz3, U4, U5, U6}, where 4 1 , U5 = Uj = U2 = u3 = ,u4 = U6 = 2 2. 4 What is…

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

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Q: In writing v as a linear combination of u ,,u, &u, ( if possible) given: y = (3,0, – 6) , u,= (1, –…

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

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Q: Find w such that 2u + v u 3w = 0. (0, 2, 7, 5), v = (-8, 4, -3, 1) 1 -- (-) W = 3 -

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Q: Let W (s, t) = F(u(s, t), v(s, t)) where W,(1,0) WŁ(1,0) = u(1,0) = -1, u,(1, 0) = −5, ut(1,0) = -7…

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Q: Let u = (1, 1), v = (3, -2), w = (4, 3), and y = ( map from R² -3, 4). Let L be a linear | to R?…

A: We know Let  Given

Q: c) Compute µr, Hy, Ož, o, Cov(X, Y), and p

A: Reviewing information, Given pdf is, f(x,y)=x+y                 ; 0≤x≤1 ,  0≤y≤1

Q: Show that R3 is spanned by S = {(1,1,1), (1, –1,0), (0, 1, – 1)}

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Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Explanation of the answer is as follows

Q: Wq = (12,3), wz=(1,3,5) not; where Determine the and w- (15,9) span R (15) span TR oY V (2,7,8).

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Q: Show that a triangle with vertices (x,Y;), (x2,y2), and (x;,y;) has area + x,y3 + X3Y, – X,Y3 – X,Y,…

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Q: Find u. (v x w). (6, 6, 6) (1, 7, 0) - (0, 0, 1) > 3

A: Given that,u=6,6,6v=1,7,0w=0,0,1