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: -4 Find the orthogonal projection ŷ of y = 4 onto the subspace 3 -3 W = Span { uj U2 = 2 Ex: 1.23

A: With the help of definition of projection of a vector on a subspace, we solve this problem.

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A: Dimension of the subspace:          If V is spanned by a finite set , then V is said to be finite…

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Q: Let W = {a + bx + cx² + dx³| a + b = 0,c – a = 0, and d – 3a = 0 } be a subspace of P3. Then the…

A: dimW = 1

Q: (c) Find a subspace U such that R³ = W₁ OU.

A: C. Hint: Use the result of part (b) in the part (c) and obtain the required result.

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

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

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

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Q: to the subspace W = Span{u1, u2} where 0. Find the distance from the vector y and u2 = -2 O 2 01

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Q: For a certain subspace W, the orthogonal projection of the vector y = 3 onto W is ŷ 2. Use this…

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Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 17, U₁ 2, U₂ = 0-16 16 24 31…

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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: [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: 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: 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: 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.

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A: Given that, -3x+2y+5z=0

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A: Subspace

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A: The following is the solved answer.

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Q: -4 Find the orthogonal projection ŷ of y onto the subspace 4 W = Span { u1 -5 Uj = u2 Ex: 1.23 : ŷ =…

A: Given

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

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A:

Q: 9. Find the vector closest to y from the subspace of Rª spanned by Vị and v2. 3 1 Vị = 1 , y = V2 =…

A: To find  The vector closest to you from the subspace of R^4 spanned by v1 and v2.

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

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

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Q: Consider the set S = y ER : 3x – 5y = 0, x + z =- . Is this a subspace of R ? Explain why or why…

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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.

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Q: ) The degree of pa is equal to the dimension of the cyclic subspace Z (a ; T) .

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Q: Find the closest point to y in the subspace W spanned by u, and u2. 7 2 y = 21 u1 2 , u2* 3 38 - 1 4…

A: Given that     y = (7,21,38) , u1 = (2,2,-1) and u2 = (-1,3,4) Here we have to find the closest…

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

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Q: For a certain subspace W, the orthogonal projection of the vector y = 5 onto W 4 is ŷ = |1. Use this…

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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: The subspace V of R4 is spanned by the vecto (a) Use the Gram-Schmidt process to find a

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Q: Let Uz?la :a,bE R and :c;d eR be two Subspaces of M, CR). Show that U eW= M, IR).

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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: Find the closest point to y in the subspace W spanned by v1 and v2 2 1 y = -2 -3] 1 2 а) b) 2 c) 1…

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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: Find the closest point to y in the subspace W spanned by vị and vz 2 1 y =| 1 |,v1 =| 0 [0] 2 lo] 2…

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