Suppose that U = leaven F,, where F is either C, R,or Q. One can show that U is a subspace of F*4- you don't have to! Find a subspace V of F4 such that F4 = UV.

Q: Let W = {a + bx + cx2 + dx c- 3d = 0} be a subspace of Pg. Then th dimension of W is equal to %3D O…

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Q: Suppose U, W,, W, are subspaces of a vector space V. Show that (Un W,) + (UnW,)Cun (W, + W,) Find…

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Q: Find the dimension of the subspace W of R* spanned by set S = {(3,0,1,–2), (–5,4,9,2), (–1,2,5,0)} .

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Q: If y is in a subspace W, then y - ŷ is not zero. Select one: O True False

A: Solve the following

Q: Show that [0,∞) and (0,∞) as subspaces of R with the usual topology are not homeomorphic.

A: Given: [0, ∞) and (0, ∞) are subspaces of ℝ. To show: [0, ∞) and (0, ∞)are not homeomorphic.

Q: show thal the set of all poiuts in the Subspace of IR 3. plane ax +by+CZ =0 is +cz = ois CA

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Q: Find the standard matrix for the orthogonal projection of R3 onto the subspace spanned by aj=(1,1)…

A: The vectors that span the subspace are a1=1, 1 and a2=0, 1. The normalising vectors are 12, 12 and…

Q: 2. How can you build a subspace of a vector space V by using a single vector vEV

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Q: Suppose U1,U;, -..Um are finite-dimensional subspaces of V. Prove that U + Uz + .. +Um is…

A: Suppose U1, U2, ... , Um are finite-dimensional subspaces of V. To prove U1+U2+ ... +Um is finite…

Q: Suppose W,, W2,. (a) span (W, W2 (b) If S; spans W; for i = 1,...,r, then S, US, U...US, spans W, +…

A: (a) W1+W2W1+W2 would be W2W2. Below is the justification.  x+y∈W1+W2,wx+y∈W1+W2where x∈W1x∈W1 and…

Q: 10. Let Y = {(x,y,z)| z=-x}. (a) Is Y a subspace of R³? Justify. (b) Is Y a vector space? Justify.

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Q: Find the orthogonal projection ŷ of y = onto the subspace W = Span { uị u2 5 Ex: 1.23 : ŷ =

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Q: Find the dimension of the subspace W of R' spanned by set S = {(-1,2,5,0), (3,0,1,–2), (–5,4,9,2)}

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Q: Find the orthogonal projection ŷ of y: 6 onto the subspace W = Span { ui u2 Ex: 1.23 ||

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Q: 4) Let x be the twor diminsional spore cquipped with the scolor product. ke subspace Yis gitn by the…

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Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = -197 1 -13 10 5 8-6…

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Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 1 -1 1 -1 1 1 1 [1] 1 II…

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Q: Find the projection of the vector v onto the subspace S. 1 1 1 S = span 1 v = projs v =

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Q: 3 show that if w is a subspace of fini a dimensional vector space y and dim (W) = dim (V) W = V.

A: This is theorem in vector spaces

Q: 2 Find the orthogonal projection ŷ of y = onto the subspace 3 -2 W = Span { ui u2 Ex: 1.23 ŷ =

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Q: Show that the set S = {(x, y) in R2 such that x =3y } is a subspace of the vector space R2 NOTE!…

A: That's easy. Have a good day!!!

Q: 1. Find the ortho gonal puojection of the Vector (1,3,1 on the subspace of IR? Spanned by…

A: Projection

Q: Suppose U1; U2; :::; Um are Önite-dimensional subspaces of V . Prove that U1 + U2 + ::: + Um is…

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Q: Find the orthogonal projection of onto the subspace W of R' spanned by -1 -1 -1 1 1 projw (7)

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Q: Find the projection of the vector v onto the subspace S. 1. S = span v = projs v =

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Q: 16 In the vector space R, let u= (1, 2, 3), v = (3, 1, 5). w = (3,-4, 7). Prove that the subspace S…

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Q: 4. Prove or disprove that the set of unit 2 vectors of R2 is a subspace of R2under usual operations

A: solve the following

Q: 5 1 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = -7 3 Ex: 5 ||

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Q: Find a basis for the subspace of R3 spanned by S. S = {(1, 3, 6), (-1, 4, 6), (2, 4, 1)} EEE

A: Basis of subspace of ℝ3 i) It must be linearly independent. ii) Its span ℝ3

Q: Show that [0, 1] and (0, 1] as subspaces of R with the usual topology are not homeomorphic.

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Q: The set { n > 1} is closed in (0, 0) as a subspace of R. - True - False I know the answer is true…

A: Given set  1nn≥1

Q: Provide a situation in where it shows a union of two subspaces of a vector space V and is not…

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Q: Q. Show that (a,b,c) where c=a+b is subspace of R

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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: projw(x) is not orthogonal to every vector in the subspace W. O True False

A: We have to check whether the given statement, "projwx is not orthogonal to every vector in the…

Q: Suppose W is a subspace of Rn spanned by n nonzero orthogonal vectors. Explain why W = Rn.

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Q: Consider X = {1, 2, 3, 4, 5} where the topology is {UC X|1 € U}. Find a subspace of X which is…

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Q: Verify that if W is a subspace of an inner product space Vand v is in V, then perpw(v) is orthogonal…

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Q: 6 Give a counter example to show that W is not subspace of R3. W=set of (x, y, z) where x + y = 1

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Q: 6. The projection of 12 onto the subspace of R spanned by ĝ V2 and a, 1 equals: -6 1,

A: 1. Let S be a non-trivial subspace of a vector space V and assume that v is a vector in V that does…

Q: Find the orthogonal projection of 10 onto the subspace W of R° spanned by 9. and 3 -1-10 3 projw (i)…

A: To find  The orthogonal projection of v onto the subspace of W spanned by the given vectors.

Q: a) Prove that W = {(a,b, 2a + b)} is a subspace of R. (more space on the next %3D if needed)

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Q: 1 SROW thet w in not a subspace 3 a Vecíor space V=R, where wis defined

A: According to our company guidelines, in a multiple questions, we can answer only first question.…

Q: Let U and W be subspaces of R³ for which dimU=1, dimW=2, and UgW. Show that R=UOW.

A: I have shown all the conditions of direct sum of two subspaces

Q: Find the orthogonal projection of onto the subspace W of Rª spanned by 1 projw (v)

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Q: If y is not in a subspace W, then y - ŷ is zeo. Select one: True False

A: If y is in subspace W, then the orthogonal projection of y onto W (y') is y itself.  And in that…

Q: 4. Find the distance from the vector j = to the subspace on R³ spanned by { 19: | }

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Q: Explain why S = {(r,y) : x, y € R, x > 0} is not a subspace of R²

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Q: )let W : aib+c+d=0f be a subie be a subse C Maa . show that W.is a subspace of )

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