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

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

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Q: T X = R with standard topology { IneN} CR k= Show that the subspace topology on k is discrete.

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Q: Let W - (a + bx + cx + dx'l a +b-0 and c - 3d = 0) be a subspace of Py. Then the dimension of W is…

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

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Q: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?

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Q: True or False: If U and W are subspaces of a finite dimensional vector space and UnW = {0}, then U°…

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Q: 9. Is Y = {(x,y, z) | y=z} R?? a subspace of

A: ψ={(x,y,z)| y=z}

Q: 10. Under the usual operations in R2, which of the following subsets is a subspace? (a) y = 2ar…

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Q: Determine is Question 2 whether W = W = {(a; z { (a; 2; 6) | α; 6ER} subspace of R

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Q: Find the closest point to y in the subspace W spanned by u, and uz. 17 1 2 %3D u1 = 0 |, u2 = - 1 2…

A: To find The closest point to y in the subspace w spanned by u1 and u2

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: Let R be the field of real numbers. Then {(x,2y,3z): x, y, z ER}is a subspace of R°(R) ?

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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: 2 -3 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = 1 %3D 8 Ex: 5…

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R. %3D

A: To Prove U is a subspace of vector space V 1) 0∈U  If x, y∈U  and a∈V  2) Closed under vector…

Q: 11) Is the set W = {f(x) E P(F): f(x) = 0 or f(x)has a degree n} a subspace of P(F) if n > 1?…

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Q: What is the dimension of the subspace W = {A = [aij] € R4x5|a45 = 0} dimW = Ex: 5

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Q: [5 Find the orthogonal projection ŷ of y = onto the subspace 3 W = Span { uį = 2 u2 3 Ex: 1.23 ŷ =

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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: .a. Is the set of vectors W = {(x,y,z) x,y,z € R,x=z+2} subspace of R³?

A: Given that a) W=x,y,z|x,y,z∈ℝ,x=z+2 of ℝ3. b) W=pt-tq of M22 Check the space W is the subspace of…

Q: (1) Suppose U and W are both five-dimensional subspaces of R°. Prove that UnW + {0}.

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Q: Suppose that X = ER' :z + y + z = 0 and ² + y² = z² Determine (with justification) whether X is a…

A: Given  X=xyz∈ℝ3:x+y+z=0 and x2+y2=z2

Q: Let  S=span(e1),  T=span(e2) and  W=span(e1+e3) be subspaces of R3.  S is orthogonal to T, T is…

A: Orthogonal Subspace

Q: Is T = {(x,y,z)| x+2 y+3z=0} a subspace of R?

A: Subspace

Q: 2. Is the set of vectors of the form a b a+2b a subspace of R³? Show your proof.

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Q: Is M = {(x,y,z)|x is nonnegative} a subspace of R³? Yes or No? Justify or give/find a…

A: Given  M =  x, y, z  x is nonnegative

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

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R?. %3D

A: Consider the given set. U=x,-x|xinR Let, consider that, f,g∈V And f, and g is defined as.…

Q: 1. Is the subset V {(x, y, z, w), y = 3z, w = 2x + 1) a subspace of R*? Show the details of %3D your…

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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: 13. Let U, W be vector subspaces of a vector space V. If dim(U) 3, dim(W) 4, dim(V) = 7 and UnW =…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Verify that U1 = {(x, y) E R² : y = -2x} is a real vector subspace of R?. hat U2 = {(x,y, z) E R³ :…

A: This a question of linear algebra and vector space.

Q: - Let V = R and W = {(a, b, c) E V \a + b = c}. Is W a subspace of V? If so, what is its dimension?

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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: Is Y = (x,y,z) | y=z} a subspace of R?

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Q: 4. Consider the vector space RR of functions f: R R. Let U = {f: R → R: f(42)=0}. Show that U is a…

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Q: 2. The subspace (a) 2y x+y+z=0 1 in R3 is a plane whose equation is x-2=0 (b) y (c). x-2y+z=0 Py27.…

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Q: (A) Let U1, U2, U3 be subspaces of M2x2(R). If V = U1 e U2 e U3, then dim V = 4.

A: So,  V is the direct sum of the subspaces U1, U2, U3  of M2×2(R) , i.e. dim(U1) = dim(U2) = dim(U3)…

Q: and uz = Find the closest point to y = in the subspace W spanned by u1 = The closest point is

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Q: 10 - What is the dimension of the subspace below? w = sp {C J. C 9 C 3 a) O 2 b) O 0 1 d) O -1 e) 3.

A: According to question  We have to calculate the dimension of the subspace.

Q: 1. Decide if the following subsets W C V are vector subspaces or not (justify) (a) W = x €RCR?. COs…

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Q: 4) Suppose u, v E V, where V is an inner product space, and ||u|| = |||| = 1 and (u, v) = 1. Find u…

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

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Q: Find the orthogonal projection ŷ of y = 3 onto the subspace W = Span { u1 = , U2 = 3 Ex: 1.23 %3D

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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: Find the projection of the vector v = [1 0 −2]T onto the subspace

A: We have to find the projection of the vector v=10-2 onto the subspace S=Span0-11,011

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

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

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