Show that U = {(x, y, z)|x – 2y − z = 0} is a subspace of R³.

Q: Prove thatII = {(x, y, z)|x – 2y+ 3z = 0}is a subspace of JR³, %3D -

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Q: Show that V is not a subspace of R°: V is the set of all (x, y, z) such that x + y +z = 3

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Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Given W be a subspace spanned by the u's, We have to write y as the sum of a vector in W and a…

Q: 3. Let W = {(x,y,z): x? + y? = z}. Is W a subspace of V = R3? %3D

A: We need to check if W is a subspace or not.

Q: Show that {f in C[a,b]:f(a)=f(b)} is a subspace of C[a,b].

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Q: 3. State why W = {x = (x1, 2, X3, T4) E R' : a1 + x2 + x3 + a4 < 1} is not a subspace of R. (H.W)

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Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y + 13 V₂ = 1 6 The closest…

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Q: 6x 1 = (2)ų pue 3 – x = (2)6 hq pelves as a co to on to a los e os (26) = projy (f) Use the inner…

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Q: Let V = {(x, y, 2x – 3y)|x, yɛR}. Prove that V is closed for addition and scalar multiplication i.e.…

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Q: Consider the subspaces U = {(x,x) | x ≤ R} and W = {(0, y) | y ≤ R} of R². Show that U + W is a…

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Q: Prove that W1 = {(a,b) E R² : 4a – b= 0} is a subspace of R2.

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Q: Produce an example of an element of Co (R, R) which is not an element of the following vector…

A: Correct answer is f(x)= Sin(x) which is infinitely many times continuously differentiable but it is…

Q: Suppose U = {(x, x, y, y) = F¹: x, y € F}. Find a subspace W of F4 such that F4 = UW.

A: Our objective is given below:

Q: -2 2 B-8-8 -2 Compute the distance d from y to the subspace of R¹ spanned by v₁ and v2. Let y = -1 5…

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Q: 2. Let V = E3 and W = {x|x = a(1,0,2) + b(1,-1,3)} and S = {x\x = (x1,x2, 1)} where a and b are any…

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Q: Which of the following sets is not a vector subspace of p? OA. W = ((x,y)x = 2y} O B. W - ((x,y)y-…

A: Subspace of a vector space

Q: defined as Let V = {(x,y) | x, y = R}, with vector addition and scalar multiplication (x₁, y₁) (x2,…

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Q: Determine whether U = {(1, s, t)ls,t e R} is a subspace of R.

A: FOR ANY SUBSET U TO BE A SUBSPACE OF ANY VECTOR SPACE V IT IS NECESSARY THAT U HAS ZERO VECTOR IN…

Q: Let S be the collection of vectors [] in R² that satisfy the given property. In each case, either…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

Q: Find a basis and the dimension of the subspace of R³: W = {(x, y, z): x - 2y + 3z = 0}

A: The given subspace of ℝ3, W=x, y, z|x-2y+3z=0. We have to find the basis and dimension of the…

Q: Let S € R² | xy ≥ 0 Y where S uses the usual definitions for vector addition and scalar…

A: Given subset of is the following :Obviously Here noted that vector addition rule : and scalar…

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

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Q: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

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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: Let W = {(x, y, 1) | x, y, E R}. Is W a subspace of R3?

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