1 Let U and V be two subspaces of R" such that UCV. Show that dim(U) < dim(V).

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

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

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Q: Find the projection of the vector v onto the subspace S. S = span 1 %3D V = 1 -1 1

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Q: 5. Show that if H and H2 are two orthogonal subspaces of H, then Hin H2 = {0}. Does the converse…

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Q: a 2. Is the set of vectors of the form a subspace of R? Show your proof

A: **As per our guidelines we are allowed to answer only one question at a time. Kindly please re-post…

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

A: Solve the following

Q: 5. Find basis for the subspace u- of R for the vector u (1,3, -4). (Here u- means %3D orthogonal…

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Q: Find the orthogonal projection ŷ of the vector y = onto the subspace W = -7 Span u =

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Q: Suppose that you wish to find the projection of u = (3,0,6)" onto the subspace W of R spanned by (2,…

A: We will find out the required solution.

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: -2 Find the orthogonal projection ŷ of y = 3 onto the subspace 2 -2 W = Span { u , U2 Ex: 1.23 : ||

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Q: 4 Let S be the subspace of R* spanned by x1 = (1,0, – 2, 1)" and x2 Find a basis for S. (0, 1, 3,…

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Q: If u and v are vectors in R and W is a subspace of R with (u - v) belong to W, then both u and v…

A: If u and v are vectors in R3 and W is a subspace of R3 with (u-v) belong to W, then both u and v…

Q: 9. Find the orthogonal projection y of y = onto the subspace 2 0. W Span u = -3

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Q: of R". SICSZ, Show that Juppose that s, and Sz are subspaces. With the thet property, dim (s.)s dim…

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Q: , dim W 5. Let U, W be subspaces of a vector space V. If dim U and Un W = {0}, what is dim (U+ W)?

A: Let V be a vector space over a field k and let U, W be finite-dimensional subspaces of V.  Then…

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

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Q: 6. Let C"(R) denote the sct of all real-valued functions defined on the real line that have a…

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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: 26. In the vector space of all real-valued functions, find a basis for the subspace spanned by {sin…

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

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Q: if a vector space is the set of real valued continuous functions over R , then show that the set W…

A: Given V is a vector space of all continuous functions over ℝ. W is a set of differential equation…

Q: Find the distance from the vector -1 y = -5 10 to the subspace W spanned by -2 1 u 0 and v= 2 ||

A: The given vector is y=-1-510 and the subspace is u=-200, v=12-1.

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

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Q: Let W be the subspace of the space of all continuous real- valued functions spanned by {cos2 t,sin2…

A: let U= cos2t,sin2t,cos2t and W be the subspace of all continuous real-valued functions spanned by…

Q: 3) Find a basis for the subspace of Pz Censistiny of all vectors of the following properties f(tD,…

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Q: Find the projection of the vector v onto the subspace S.

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Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

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

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Q: Let V be the subspace of C[a, b] spanned by1, ex, e−x, and let D be the differentiation operatoron…

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

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Q: 3. Is the set of all vectors (x, y) in R2 with the usual addition and scalar multiplication, a…

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Q: W= im T when W is a T-invariant subspace, and V=ker + W. Where V is finite dimentional, when you let…

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

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Q: 2 Find the orthogonal projection of u = onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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

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Q: In R, let S be the set of all vectors with third component 0. { a S = ER Show that S is a subspace…

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Q: 5. Find basis for the subspace u- of R for the vector u = orthogonal subspace of u) (1,3,-4). (Here…

A: As we know that S=v1,v2,...vk be a set of vectors in Rn  then S is called an Orthogonal if and only…

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 ŷ of y = -5 onto the subspace 6. -2 W = Span { uį 4 3 u2 %3D -2 Ex:…

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Q: If B is basis for (x, t) then By = {BnY/BE basis for the subspace topology Ty on y IS 9

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Q: 2 Find the dimension of the subspace H of R spanned by – 12 8 ..... dim H =

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

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Q: (5) Suppose that T E L(V) is such that all subspaces of V of dimension dim(V) – 1 are T-invariant.…

A: Please check step 2 for the solution.!

Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors u;. are orthogonal.)…

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Q: Suppose U and W are subspaces of V for which UUW is a subspace. Show that UCW or W CU.

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