Find the orthogonal projection ŷ of the vector y = onto the subspace W = Span u 2 Ex: 5 C ŷ = %3D

Q: Q2) Let W be a subspace of R* and its orthogonal complement is given by W+ = span find an orthogonal…

A: The basis of  W⊥ is given  From this we have to find the basis of W. Let x=x1,x2,x3,x4∈W Then…

Q: Is W a subspace of the vector space V? Justify your answer. 1. Wis subset of V = R3 where a W = {…

A: I just used a test of subspace to check the W is subspace

Q: Find the closest point to y in the subspace W spanned by v, and v2. 13 1 5 - 1 y = 1 1 , V2 = 1 - 1…

A: Given y=13-112,v1=11-1-2,v2=5103. The orthogonal projection of y onto span of v1, v2 is…

Q: Which of the following are subspaces of R^3?  W ={(x, y, z) :x+y+z=0}

A: Given, W=x,y,z:x+y+z=0 Let, 2,-1,1∈W Let, -1∈F

Q: _. Let u = 6 " and let W be the set of all x in R3 such that u x = 0. (a) Show that W is a subspace…

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Q: Let H = Span{₁,..., If u € R¹ satisfies vú = v½ u then u belongs to H¹. p} be a subspace of R" . =…

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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: (a) find the orthogonal complement S⊥, and (b) find the direct sum S⊕S⊥. S is the subspace of R3…

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Q: Find a basis for the given subspace of R° , and state its dimension for the plane 4 x - 2 y + 5 z =…

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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: 3. For a certain subspace W, the orthogonal projection of the vector y = |4 onto W 5 is ŷ = | 0 Use…

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

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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: 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 T : U = р — 2q — 0, р, 9, r, s E R Is U a subspace of M2.2(R), if so, find its basis and…

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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: Let V = P2(t) with inner product defined by (f, g) = So f(t)g(t) dt. Find a basis for the subspace W…

A: An inner product is a generalization of the dot product. A real vector space, an inner product…

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: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y? + z²) = 0. Is V a subspace of R?

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

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Q: Let W = (a + bx + cx? + dx³la + 2c 0 andb-d D 0) be a subspace of P,. %3D Then dimension of W is…

A: Given  W={a+bx+cx2+dx3| a+2c=0 and b-d=0}Since a+2c=0⇒a=-2cand b-d=0⇒b=dwhich gives…

Q: Find the orthogonal projection of V = nto the subspace W of R* spanned by Uj = U2 = Uz = -6/4 -6/4 w…

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Q: Find the closest point to y in the subspace W spanned by vị and vz 2 y =| 1 ,v1 0,v2 -2 2 а) b) c)…

A: The following is the solved answer.

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

Q: Is W = ((x,y) | xy=0} a subspace of R??

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Q: The answer above is NOT correct. Find the orthogonal projection of 20 onto the subspace W of R…

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

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Q: Find the dimension of the subspace U = {[x, y, z, t]|x+4y-z = 0; x-2z+ t= 0}. Select one: а. 4 b. 2…

A: Given subspace is U = {[x, y, z, t] | x+4y-z = 0;x-2z+t=0}

Q: Find the projection matrix P that projects vectors in R onto W Let W be the subspace of R spanned by…

A: The inverse of a 2×2 matrix is calculated using the formula: a  b c  d -1=1deta  b c  d d  -b -c  a…

Q: 1 1 onto the subspace W = Span -7 Find the orthogonal projection ŷ of the vector y = u = 2 Ex: 5

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Q: H 6 and let W be the set of all x in R3 such that u x = 0. (a) Show that W is a subspace of R³. (b)…

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Q: Consider the set S = yl E R : 4x +6z=7y, x – 13y=0 . Is this a subspace of R ? Explain why or why…

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Q: Q3. Point a base of this subspace of R*: W = { (x,y,z,t) ||-y+z=0,t - = 0 }

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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: 5b + 2c Let W be the set of all vectors of the form where band c are arbitrary. Find vectors u and v…

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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: W e R"|2, > 0 over the field of reals is a subspace of the specified vector space ER"

A: Given that W=x1x2x3⋮xm∈Rm|x1≥0 and V=x1x2x3⋮xm∈Rm The objective is to show that W is subspace of V.…

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: Let W be the subspace spanned by u, and u,. Write y as the sum of a vector in W and a vector…

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

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Q: Let U = Span{6, sin? (6x), cos²(6x)} be a subspace of the vector space of real-valued functions…

A: According to the trigonometric properties, cos26x=1-sin26x Thus, cos26x and sin26x are linearly…

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: Show that U = {(r, y, z): r.ye R} is a subspace of R³. Then, find a linear complemen

A: Here a subset of ℝ3 is given as U=x, y, x: x,y∈ℝ

Q: Let W be the subspace of R spanned by the vectors 3 and -6 12 Find the matrix A of the orthogonal…

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

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