can we have a polynomial Q(x,y,z) such that the subspace {(x,y,z):Q(x,y,z)=0} is a smooth submanifold diffeomorphic to T^2(torus)

Q: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R}…

A: (a), (b) , (c), (d)  are subspaces .

Q: You are buying a car. Would you prefer a higher rate for a lower term or a lower rate for a longel…

A: Given that You are buying a car. Would you prefer a higher rate for a lower term or a lower rate for…

Q: 4) Which of the following is a subspace of R^3? Justify your answer. i) W={(x,y,z)|x+y+z=0} ii)…

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Q: Find the Kernel and Range of the linear transformation L : R^3 → R^3 defined by L(x) = (x3, 0,…

A: In linear algebra, the kernel of a linear transformation is also known as the "null space." Given a…

Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: Wi = {(a,b,c,d) E R* : a+ b+ c = 0} ve W2 = = 0, b = 0}, Being subspaces of R^4 {(a,b,c,d) e Rª : a+…

A: For the given subspaces W1 and W2, we have to calculate…

Q: Let a be a fixed unit length vector (A is in R^3). Define a linear transformation T: R^3 -> R^3 by…

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Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw() = 4 6 V= 19 16 and -5

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Q: Find the orthogonal projection of 7 = projw (u) = -251 17 2 31 onto the subspace W spanned by []} 2…

A: W is a 3 dimensional subspace.

Q: 6. Determine if {(x, y): x^2 + y^2 ≥ 8} is a subspace of R^2

A: The given set is {(x, y) | x2 + y2 ≥ 8}. We check whether the set is a subspace of R2.  Since the…

Q: For any fixed vector v in R^n, the set V=?x∈R^n :v^(T)x=0 is a subspace of R . Assuming v does not…

A: According to the given information, Let V be a fixed vector in Rn, the set V is given as:

Q: Which of the following sets is not a subspace of the space R^3? (a) R^3. (b) Any plane passing…

A: Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: Find a vector valued function which gives the curve of intersection of  y2 + z2 =16  with the plane…

A: Given the curves:

Q: b. Determine whether the statement is true or false and justify your answer. Determine which of the…

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Q: Write the equation of a subspace that passes through a point a ∈ R^d and is orthogonal to a given…

A: Let d=3  Now we will find the equation of subspace that passes through a point a€R^3 and orthogonal…

Q: Consider the vector space R^n with inner product

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Q: If U = {(x, y, z) : 3x -y-2z = 0} is a subspace of R, then U = %3D %3D %3D A) {(r, y, z) : r - y+ =…

A: Given  U={(x,y,z): 3x-y-2z=0}is a subspace of R3 To find the value of U⊥

Q: Is S = {(x1, x2)^T ∈ R^2| x1 > x2} a subspace of R^2? Justify your answer.

A: Solution:Given: we have to check that is a subspace of or not.

Q: The percentage of female high school graduates who enrolled in college is given in the table below.…

A: Let x represent time(in years) since 1970, and let y represent the corresponding percentage of…

Q: Suppose V is finite-dimensional and U and W are subspaces of V with W^0 ⊂ U^0. Prove that U ⊂ W.

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Q: Show there is no proper five dimensional subspace of R^5. (i.e. If V is a subspace of R^5 with dim…

A: To Show: If V is a subset of ℝ5, with dimV =5 then V=ℝ5.

Q: Let vl ་ མ། 2 - - ་ -2 and determine if w is in the subspace of R³ generated by v¹ and v². Show your…

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Q: show what W = {(a,0,b)| a,b E R)  is a subspace of R^3

A: Given : W={(a,0,b)|a,b∈R}   To Show : W is subspace of R3

Q: Let C[0, 1] be the vector space of continuous functions that are defined on the interval [0, 1].…

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Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = --B 7 010

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Q: Is W = ((x,y) | xy=0} a subspace of R??

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Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (7) 0 -8 v= 0 0·00 ||

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Q: Don't change the W subspace. It is  W = {(x,-x, 2x): x, y ≤ R}

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Q: ) Consider C with the usual inner product, given by (u, v) = ₁₁ + The vectors are orthogonal. Let…

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Q: a) Is the set W = {(x, y, 1) | x, y are real numbers} a subspace of R^3 ? (b) Is the set W = {(x,…

A: Subspace test:  Let V be a vector space and W is a subset. The subset W is said to be subspace if it…

Q: U = {(z,w) ≤ C² : z²+u²=0}, W={(z,w) ≤ C² : Re(z) = Re(w)} Are subspaces of C²?

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Q: Create a vector-valued function whose graph is an ellipse, centered at (1, 2) with horizontal major…

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Q: If W is a subspace of R" and ax is in W, where a is a nonzero scalar and x is in R". Then x is in W/…

A: We have to check