3i There will be: U = {p(x) e R4[x]]p(0) = p(1) = p(2)} Proved that U is a subspace of R4[x] and find a finite Linear span for it.

Q: (b) If V = U OW is a direct sum of subspaces U, W C V then any element v E V can be written uniquely…

A: Given V=U⊕W is a direct sum of subspaces U,W⊂V.  Then, it is known that any element v∈V can be…

Q: Find the orthogonal projection of - -1 1 12 2 || subspace W of R4 spanned by -1 1 1 = 0 7 0 1 1 " −1…

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Q: 1. Let e Z(X) and let A = {xe X: f(x)=x}. Show that M is a subspace of X.

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Q: Let y d = = -4 -6 -3 V1 || 1 -2 -4 1 V₂ = 0 2 -1 -1 4 Compute the distance d from y to the subspace…

A: I am going to solve the problem by using some simple algebra to get the required result of the given…

Q: Suppose Vis finite-dimensional, T = L(V), and U is a subspace of V. Prove that U and U are both…

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Q: Use the inner product = = f(x)g(x)da in the vector space Cº [0, 1] to find the orthogonal projection…

A: Given: The functions are fx=2x2+4, gx=x-12 and hx=1. The inner product is given by f,g=∫01fxgxdx in…

Q: B 1 Find the dimension of the subspace V span{v1, v2, V3, v4} in R³ where vị = 2 1 V2 = , V3 = and…

A: We find dimension of the subspace V

Q: B 6. Which of the following is a subspace of R³? a. {(x,y,z)/x-3y-1} b. {(x,y,z)/x=3y+1} c.…

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Q: Let U be a subspace of the vector space P100 (R), with dim(U) = 37. Suppose W is another subspace of…

A: P100(R) is a vector space  of all polynomial of degree 100 and smaller. The dimension is 101.For…

Q: 4. Let W be the subspace of R³ spanned by w the orthogonal projection of 8- onto W. - (2/3) 1/3 and…

A: orthonormal vectors:- A set of non zero vectors v1, v2, v3,......, vn is called orthonormal if…

Q: M2x2 (R) is a vector space over R. Make use of this result to show that the subset S defined by a S…

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Q: Let Z E R³ | y Prove that Z is a subspace of R³. = Z

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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: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (v) = - C 12 = 0 2 0

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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: 4. Let S be the subspace of P₂ defined by S = span{1 − x, 1 + x, 5, 1 – x², 2x}. Find dim(S), and…

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Q: Use the inner product = = f(x)g(x)da in the vector space Cº[0, 1] to find the orthogonal projection…

A: Given,         f(x)=2x2+4,     g(x)=x-12 and  h(x)=1. To find                  projvf=?.

Q: Let W be the subspace of R4 spanned by T1 = (1) Which linear functionals f(x1, x2, x3, x4) = C₁x₁ +…

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Q: Suppose T = L(V) and U CV is a subspace which is invariant under T. Prove that U is invariant under…

A: The answer for the given question has been solve step by step below please find the attachments…

Q: Which of the following subsets is not a vector subspace in the vector space R2[r]?

A: The correct option is:e){ a+bx∣a+b−1=0}Explanation:

Q: Is the set W = {f(x) = P(F) : ƒ(x) = 0 or f(x) has degree n} a subspace of P(F) if n ≥ 1? Justify…

A: Set : W= fx∈PF : fx=0 or fx has degree n

Q: -(80) (b) 2. The subspace (a) x+y+z= By in R³ is a plane whose equation is x-2=0 (c) y x-2y+z=0 (d)…

A: Here i am using linear combination and then we saw the relation between the coordinates.

Q: (3) Is Mmxn(Q) is a vector subspace of Mmxn (R) over R?

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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: Show that V = W₁ © W₂ for the given vector space V and the given subspaces W₁ and W₂. (a) V = R³, W₁…

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

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Q: ts) Let P2 denote the vector space of polynomials of degree up to 2. Which of the following subsets…

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Q: 9 9 -10 Find the orthogonal projection of v [8] Note: You can earn partial credit on this problem.…

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Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw(7) = = -15] -8 v = -16…

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Q: 1. (- Let W₁ --E--E) and W₂ = = 1 -1 (a) Find a basis for W₁ W₂. What is dim(W₁ W₂)? (b) Show that…

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Q: 6) Suppose U = {(x1,x2, ...) E F®|x; # 0 for only finitely many j}. (a) Show that U is a subspace of…

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Q: 3. Consider V = {a2x² +a1x + ao € P2(R) : a2 + a1 + ao = 0} . Use the subspace theorem to show that…

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Q: 2) Let V=R²³: W= { x = (X₁₁ X ₂₁ X 3) ER ³²: 2x₁ - x₂ + 5*3=0}. Prove that W is a subspace and find…

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Q: 31. Let W be the subspace sp(sin 2x, cos 2x) of the vector space of all real-valued functions with…

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Q: Let W = { |xy <0}. Is W a subspace of R?? If so, use generic terms to demonstrate the necessary…

A: W is not a subspace of R2.

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by 7 = ㅜㅜㅜ 0

A: We have to find the orthogonal projection of  onto the subspace   spanned by

Q: Q # 2(b) Let X (a, b) and Y (0,1) be two subspaces of R (with the usual topologies). Prove that X…

A: Given that X=a,b and Y=0,1 be two subspaces of R. We say that X and Y are homeomorphic if and only…

Q: Recall that P₂(R) is the vector space of all polynomials of degree at most 2 with coefficients in R,…

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