12- Let X=C[0,1] and let W=[fo,f1,...] such that f;(x) = x', then we have W is A-an infinite subspace and not closed B-an infinite subspace and closed C-a finite subspace and not closed

Q: 2. Let S be the subspace of R5 spanned by x = (1, , (a) Find a basis for S- (b) Give a geometrical…

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Q: 5 9. and define p : R² → R² by p(x) = Ax (that is, p = PA). Find Let A -1 -1 all 9-invariant…

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Q: CLEICE If (Y, Ty) is a subspace of (X, T). Then each open set in Y is open in X if I only if Y is…

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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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: 1 -2 Let W = Span -1 1 be a subspace of R4, and let w - be the subspace of Rorthogonal to W. Then…

A: Here no need to use the given vectors.. We need only the dim of W

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

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Q: 1 -1 Find the distance from y to the subspace spanned by u. U= y= NO N1

A: Here given vectors are: u=2021y=1-11-1

Q: 6. Let U and W be 3-dimensional subspaces of a 4-dimensional vector space V, and suppose that U # W.…

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Q: Theorem 6.8. Let A be a closed subspace of a compact space. Then A is compact.

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A: The dimension of a nonzero subspace H, denoted by dim(H), is the number of vectors in basis for H.

Q: (a) Let S and T be subspaces of a vector space V. Show that SUT is again a subspace of V if and only…

A: As per policy I can solve only one question. Please repost other question.

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

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 7. Let W span{x} be a subspace of P2(R) with (p(x), q(x)) = p(x)q(x) dx. Find W-.

A: I am solving this in step 2

Q: 3 1 Show that the null space of A is a 02 subspace of R³. Which subspace can you obtain by the…

A: It is given that,  A = 13-1024 We have to show that the null space of A is a subspace of ℝ3 and to…

Q: 4. Let S be the subspace of R4 spanned by x = (1,0,-2,1)7 and x2 = (0,1,3, -2)T. Find a basis for S

A: Consider a matrix A as follows.

Q: 3- The interval (0,1) in (R, T;) is: a- Compact subspace, b- Connected subspace, c- Both a and b, d-…

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Q: Suppose that U = leaven F,, where F is either C, R,or Q. One can show that U is a subspace of F*4-…

A: Given that U=xxyy∈F4 x,y∈F is subspace of F4, where F is either ℂ,ℝ, or ℚ. Since: U=xxyy∈F4…

Q: 6. (a) Determine whether the set of all vectors of the form (a,b,c), where b a+c, is a subspace of…

A: The subspace of R3 is (a,b,c) where b=a+c

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: 3. Let A be an arbitrary m x n matrix. Consider all x's, such that Ax = 0, and show that the set of…

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A: Given that P2 be the vector space of all polynomials of degree 2 or less, and H be the subspace…

Q: Theorem 6.9. Let A be a compact subspace of a Hausdorff space X. Then A is closed.

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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: Determine whether the subset of C(-∞, ∞) is a subspace of C(-0, ∞) with the standard operations The…

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Q: 2- Let H be a Hilbert space. Prove that for any two subspaces M,N of H we have (M+ N)+ M'ON. OTON…

A: Let , H be a Hilbert space. We have , M  and  N are two subspaces of H. We need to prove that , M +…

Q: 1) Recall that F" is a vector space for any n. Letting n = 1, we see that F is also a vector space.…

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Q: (b) Define subspace and Verify whether is subspace v = {(x,y,2):x,y,2ER² and x-2y+3z = 5}

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Q: -3 x = -4 and y Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of…

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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Q: 6. (a) Suppose U, W are subspaces of V. Show that (U + W)° = U°nW°. (b) Suppose V is…

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Q: Determine whether the subset of C(-0, co) is a subspace of C(-0, co) with the standard operations.…

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Q: 3. If A and B are finite-dimensional, orthogonal subspaces of an inner product space V, then show…

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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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: |412 = -a}, verify that S'is a 7. Let S subspace.

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Q: 14) Find all values of h such that y will be in the subspace of 3 spanned by v1, v2, v3 if vị = 2,…

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Q: 8) Describe geometrically all subspaces of R" for n 1, 2, 3.

A: We will do this for all three parts; n = 1, 2, and 3 (in as clear handwriting as possible)

Q: The set of all points in R3 satisfying x + y - z = 0 is a subspace. Note that the set of point…

A: It is known that any subspace of ℝ3 should contain an additivities identity element 0, 0, 0.

Q: Q2. Let V be a vector space over a field (F, +, .), let M1 , M2 and M3 be subspaces of V. Prove or…

A: V be a vector space over a field (F,+, .) , M1 ,M2 and M3 be the subspace of V

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: 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: (a) A subspace Y of a Hilbert space H is closed if and only if Y = Y.

A: To Prove- A subspace Y of a Hilbert space H is closed if and only if Y⊥⊥ = Y.

Q: [2] --31 Let W be the subspace spanned by 2 5 Find an orthonormal basis for W.

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A: We will find out the required solution.

Q: 6. (a) Determine whether the set of all vectors of the form (a,b,c), where b = a+c, is a subspace of…

A: To show the subset W is a subspace , we need to show that (a) 0∈W (b) For every w1 , w2∈W , we have…

Q: 3.) Determine whether the set of odd fuction: f (-x) = -f(x) which is a subset of C(-∞,0) is a…

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Q: Let X = R and Y = (-1,1) have the subspace topology inherited from R. The spaces X and Y are…

A: In the given question given that X=R and Y=(-1,1) have a subspace topology. we know that a…

Q: 12- Let X=C[0,1] and let W=[fo,f1...] such that f;(x) = x', then we have W is A-an infinite subspace…

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