Find a basis for the given subspace of R’, and state its dimension for the plane 4 x - 2 y + 5 z = 0 Vi = 1 V2 = 1 0.8 0.4 1 V1 = V2 = 1 0.8 0.4 1 1 V1 = 1 V2 = 1 -0.8 0.4 1 Vi = V2 = 1 -0.8 0.4 1 Vi = 1 V2 = - 0.8 0.4

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: Find a basis for the subspace of R^4 that is spanned by the vectors v1 = (1, 1, 1, 1), v2 = (2,2, 2,…

A: Let us consider set S then the set S is  linearly independent or dependent  Determine the linear…

Q: Find the dimension of the subspace H of IR2 spanned by the vectors and

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Q: The sets B={[1 2 2 1]T;  [1 0 2 0]T;  [2 0 4 -3]T} and B'={[0 2 0 1]T;  [2 1 4 -1]T;  [1 2 2n 4]T}…

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Q: Show that the solution set to a system of equations of the form a + a, x = 0 + an x = 0 a m, + ... +…

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Q: 1

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Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw (v) |||| 6 V H 14 2 and…

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Q: Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R spanned by V1 = (1,…

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

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Q: |Find basis for the set of vectors in R²on the line y = nx. where n is last digit of your arid…

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Q: If u and v are vectors in R and W is a subspace of R with (u - v) belong to W, then both u and v…

A: If u and v are vectors in R3 and W is a subspace of R3 with (u-v) belong to W, then both u and v…

Q: Find the basis for the given subspace of R°, and sta its dimensions for the plane 2x – 4y +5z =0. 1…

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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: 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: dimension

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Q: Use the Gram–Schmidt process to find an orthonormal basis for the subspace of R4 spanned by x1 =…

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

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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: Find the orthogonal projection of the vector v onto the subspace S. v = |2 S =

A: projS(V) = (u1.v/u1.u1)u1 + (u2.v/u2.u2)u2

Q: Find a basis for the given subspace of R , and state its dimension for the plane 2 x - 4 y+ 5 z = 0.…

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Q: Find a basis for the subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]). Show your work, and…

A: We find basis of subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]).

Q: if a vector space is the set of real valued continuous functions over R , then show that the set W…

A: Given V is a vector space of all continuous functions over ℝ. W is a set of differential equation…

Q: Let u, = 2 |, u2 and uz = 0 Note that u, and uz are orthogonal but that uz is not orthogonal to u,…

A: The orthogonal vector is given as follows :

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

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

Q: Find the projection of the vector v onto the subspace S.

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Q: Find a basis for the solution subspace Ax=0 where A=[-2,4; 1,-2] OA. {(1,0),(0,1)} O B. {(1,2)} C.…

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Q: Find a basis of the subspace of R defined by the equation 6y, + 3y, – 4y, = 0 Basis:

A: Given data÷

Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

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Q: 2, Find bases for the fundamental subspaces; R(A), R(A"), N(A), and N(A"), given the matrix 1 -2 2 A…

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Q: Find a basis for the given subspace of R°, and state its dimension for the plane 3 x- 2 y+ 5 z = 0.…

A: We have the vector space R3 , the subspace here is: W={(x,y,z) | 3x-2y+5z=0 ; x, y, z∈R}

Q: determine the dimension of the subspace of R3 spanned by the given vectors.

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Q: Find the subspace generated by the vectors A= (2,1,-5), B= (4,3,7) %3D %3D So in space R³

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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: ) Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: First we need to write given vectors in matrix form and try to use row reduced echelon form(RREF) :

Q: Find the basis for the given subspace of R°, and state its dimensions for the plane 2x - 4y +5z =0.…

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Q: Find a basis for the subspace and state the dimension. p– 2q 2р-5r :P,q,r e R а. -2q +2r -Зр+ 6r| 1…

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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: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

Q: Find the orthogonal projection of u = 1 onto the subspace of R³ spanned by the vectors - 3 2 V1 =…

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Q: Find the basis for the given subspace of R°, and state its dimensions for the plane 2x – 4y +5z =0.…

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Q: Find the dimension of the subspace W of R4 spanned by S = {v1, v2, v3} = {(−1, 2, 5, 0), (3, 0, 1,…

A: Dimension of a subspace W is given by the number of linearly independent vectors in the basis of W,…

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: Find the orthogonal projection ŷ of y = -5 onto the subspace 6. -2 W = Span { uį 4 3 u2 %3D -2 Ex:…

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

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Q: Find a basis for the given subspace of R°, and state its dimension for the plane 2 x - 4 y+ 5 z = 0.…

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

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Q: 2. Find a basis for the subspace W = {[x y z]T : ax + by + cz = 0, a,b, c € R} of R". What is the…

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