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: (3) For each of the following sets, determine whether it is linearly independent or dependent. (a)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: The subspace defined by H = ((2,0,1), (2, -3,0)) in R3 T:R3 → R4, T(x, y,z) =…

A: Consider the given information: H=2,0,1,2,-3,0 be the subspace in R3. T:R3→R4 defined by,…

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

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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: Let f(x) = −4, g(x) = -5x+7 and h(x) = - -2x29x+9. Consider the inner product (p,q) = p(-1)g(-1) +…

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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: Consider the subspace spanned by B = {cos(x), sin(x), x cos(x), x sin(x)} inside the space of…

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

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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: (i) Consider the vector space M2×2 with the trace inner product ( A,B) = trace(A'B) and let A = .…

A: We are entitled to solve only one question at a time. Given - To find -

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: 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: 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: Determine if W is a subspace of R³, and show why or why not

A: In this question, we have to check the given set is subspace or not

Q: Consider the subspaces U = ((1, 0, 0), (0, 1, 1)) and W = ((1,2,3)) of the vector space R³. [Note:…

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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: Let V be a vector space, and let T : V → M₂2 be linear. Let V₁, V₂ EV and suppose 2 T(v₁) = J 1…

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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: Find a basis for the following subspace of Rª over R: 3 1 4 7 span 10 11 13 What is the dimension of…

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Q: Let V be P2 with the inner product given by evaluation at -2, -1,0,1 and 2. Let p1(t) = 1 + 3t,…

A: Given: Let V be P2 with the inner product given by evaluation -2,-1,0,1 and 2              Let…

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: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = TT +-18]

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Q: Let V = P2(Q), the vector space of polynomials of degree at most 2 with rational coeffi- cients,…

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Q: 4. 2ydx + (x a'y) dy = 0

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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: 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: 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: Describe explicitly a linear transformation from V, (R) into V, (R) which has its range the subspace…

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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: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (v) = 16 -20 -6 = 16 9…

A: We have to find the orthogonal projection of onto the subspace W of R4 spanned by Let v1 = and v2 =…