#6. Let W be the subspace of R³ spanned by the two vectors (1, – 1,1) and (3, – 2,0). Which one of the following vectors is a basis for W, the orthogonal complement of W? (A) (1, 1, 0) (B) (- 1,0, 1) (C) (1, 2, 1) (D) (2, 3,0) (E) (2, 3, 1)

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.

Q: A. 2. Find the Basis of the following subspaces of R3: (a) the Plane 5x - 4y+3z 0 (b) the line r= 6t…

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Q: 1)Let W CR³ be the subspace generated by the vectors (1, 0, 1)and(1, 1, 0). a )Find the orthogonal…

A: Given W⊂R3 be the subspace generated by the vectors (1,0,1) and (1,1,0). Solution a: Since every…

Q: The vector x is in a subspace H with a basis B = (b, ,b2). Find the B-coordinate vector of x. - 1 ,…

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Q: 1. Let B = be a 1 basis for the subspace V. Find the matrix that projects any 4 vector v E R* onto…

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Q: Let W = {(0,x, y, z): x + 6y – 9z = 0 } be a subspace of R*. Then a basis for W is: {(0,6,1,0),…

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Q: 5. Consider the vectors in R³, and let W be the subspace Span{x1,x2}. (a) Find an orthogonal basis…

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Q: Let W be the subspace of R$ spanned by the vectors w,=(2, 2, -1, 0, 1), w2=(-1, -1, 2, -3, 1),…

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Q: Use Theorem 5.2.1 to determine which of the following are subspaces of R3. (a) all vectors of the…

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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: The vector x is in a subspace H with a basis B = {b, ,b2}. Find the B-coordinate vector of x. 1 -3…

A: According to the given information, X is a vector in a subspace H with basis B. it is required to…

Q: The vector x is in a subspace H with a basis B= {b, ,b,}. Find the B-coordinate vector of x. 1 -3 -…

A: We will solve a system not equations to find the B-coordinate vector. The detailed solution is as…

Q: Let S be a subspace of R with basis B={[0,1,-3], [3,3,0]) The coordinate vector of v=[-15,-20,15]…

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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: a) In the vector space R3, let a = (1,2,1), ß = (3,1,5),y = (3,–4,7). Show that the subspace spanned…

A: We can solve this by finding the reduced row echelon form. We also know that elementary row…

Q: The set {V₁, V₂} is a basis for a subspace W of R4. Find the orthonormal basis {u₁, u₂} obtained by…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Q5. Find an orthonormal basis of the subspace spanned by the vectors 1 3 3 121C

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Q: The vector x is in a subspace H with a basis B = {b, ,b2}. Find the B-coordinate vector of x. %3D 1…

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Q: Let W = {(0, x, y, z): x + 6y- 9z = 0} be a subspace of R. Then a basis for W is: O (0,6,1,0),…

A: Basis for a subspace of a vector space

Q: 2. Consider vectors of the form 2y + 5y 4y 3x + + 5z] 2х 8z ,x, y,z are real # - W = -x + 7z y +…

A: Solve the following

Q: -3 Find the orthogonal projection ŷ of y = -1 onto the subspace -2 5 W = Span { u1 = -5 u2 = -3 Ex:…

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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

Q: -5 -1 and v = 9 Let vi = Let W be the subspace spannd by the u's. Use the -9 3 Gram-Schmidt process…

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Q: Find a basis for the subspace of ps W= , X3, X4, Xs )x1 + 2x, + x5 = 0} OA {(1.0,0,1). (0,-1,0,0,2).…

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Q: 2. Let W be the subspace of R5 spanned by the vectors (1,1,1,1,1),(1,0,1,0, 1), (0,1,1,1,0),…

A: For the solution of the problem follow the next steps.

Q: Let 3 -7 ,V = u -3 -3 4 and let W the subspace of R* spanned by u and v. Find a basis of w', the…

A: The given vectors are u=3-73-3, v=-12-34 and W be the subspace of R4 spanned by u and v.

Q: Find a basis for the subspace given by the plane −3x + 2y + 5z = 0.

A: we have to find a basis for the subspace given by −3x +2y + 5z = 0.

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: The vector x is in a subspace H with a basis B = {b, ,b,}. Find the B-coordinate vector of x. 1 - 2…

A: Given that, b1=14-2; b2=-2-73; x=15-3 Since B = b1, b2 is the basis, xB is the linear combination of…

Q: Let W = {(x,y,z): x – 6y + 8z = 0 } be a subspace of R³. - Then a basis for W is: O…

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Q: 2r Let U = |r,s eR Then U is a subspace of R3. %3D .3s Find a basis of U, and calculate dim(U).

A: We have given U=2r-r3s|r,s∈ℝ Then, 2r-r3s=r2-10+s003 Therefore, we can write any vector of U in the…

Q: 3) Find a basis for the subspace of R that consists of the intersection of the planes X-3Y = 5Z and…

A: This is a problem of vector space.

Q: ue 1. If the set of vectors U is linearly independent in a subspace S then vectors can be added to U…

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Q: 2 2 , find the closest point to v in the subspace W spanned by 6 and 3 Given i = 6. 1 12

A: To find  The closest point to V in the subspace spaneed by the given vectors.

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: 34. Let W be a subspace spanned by u₁ = (1, 1, 1) and u₂ = (-2, 5, -3). Write vector.orthogonal to…

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Q: Question3: Find a basis for the subspace W of R4 spanned by the set of vectors 1 0 - 1]; v2 = [0 1 2…

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Q: a 6. Let H be a subspace of M2x2 whose vectors are of the form Then, B 2 is a basis for H. 7 Find…

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Q: 1 4 Let 3= {b1, b} be a basis of a subspace H or R3, where b, = 5 1. b, = -7 If x = 4 is a vector in…

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Q: 6. Let S be the subspace of R3 that consists of all solutions to the equation x+5y−z = 0.Find a…

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Q: Let W = {(x, y, z): x - 6y + 9z =0) be a subspace of R3. %3D Then a basis for W is: O…

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Q: 1 1 11. Find a basis for the subspace of R4 spanned by u1 = U2 = U3 and -3 1 1 1 U4 =

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Q: 1) LetF1 be the subspace generated by the vectors (0, 1, 1), (0, 0.1) and 2 the subspace generated…

A: In this question, concept of subspace is used. Subspace A subspace is a vector space that is…

Q: Question3: Find a basis for the subspace W of R4 spanned by the set of vectors vz = [1 1 0 - 1]; v2…

A: A basis for a subspace is the minimum number of vectors which span the space and are linearly…

Q: Let H span {(-13, –1, -3),{-9,2, –2), (-1, –5, 0)}. A basis for the subspace H C R³ is { }. vector…

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Q: The cosine space F3 contains all combinations y(x) = A cos x+ B cos 2x+C cos 3x. Find a basis for…

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Q: Let W = {(0,x, y, z): x – 3y + 9z = 0 } be a subspace of R*. Then a basis for W is: {(0,3,1,0),…

A: A basis B for a vector space V is a linearly independent subset of V that generates V.  And the…