1 -1 Find the distance from y to the subspace spanned by u. U= y= NO N1

Q: [0, 00) (with the subspace metric) and A= [0, 1). Then aA = {1}.

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Q: 2. Let S be the subspace of R5 spanned by x = (1, , (a) Find a basis for S- (b) Give a geometrical…

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Q: 12 - 1 and v2 = Find the distance from y to the subspace W of R* spanned by v, and v2, given that…

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Q: - 15 - 13 -1 Let y = and v2 Find the distance from y to the subspace W of R“ spanned by v, and v2,…

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Q: 22.13 Suppose A =|1 2 and b=0 3 Compute x = (ATA)-'A*b, P= A(ATA)-A", and Ax Pb. What is the…

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Q: 1 Given v = -1 4 find the coordinates for v in the subspace W spanned by -7 -4 2 3 -2 u1 = 1 , u2 =…

A: The vectors u1, u2, u3, u4, u5 are orthogonal. Therefore, ui·uj=0, for i≠j. Consider the given…

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: 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: 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: -10 e subspace W of R" spanned by 6 and 3

A: In this question, concept of orthogonal projection is applied. Orthogonal Projection Matrix of…

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 -6 -4 -3 4 Let y = V1 = 1 5 -1 Compute the distance d from y to the subspace of R4 spanned by v₁…

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Q: Question 4. If U is a subspace of R", show that U-- = U.

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Q: Soal 1. 35. Find the closest point to y = (3,-1, 1, 11) in the subspace W spanned by V₁ = (1,-1,-1,…

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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 B = {1, x, eX, xe*} be a basis for a subspace W of the space of continuous functions, and let Dx…

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Q: 1 Let U and V be two subspaces of R" such that UCV. Show that dim(U) < dim(V).

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 7 Given v = -1 1 find the coordinates for v in the subspace W spanned by -1 4. U1 -2 and uz = -2 -2…

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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: orthoganal basis for the subspace Determire an C E-M/2, R/2] spanned ley E1, sinx ,cosx3

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Q: 5. Let W₁ = equal to (a) 0 and W2 = (b) 1 0 be subspaces of R³. Then dim(W₁ W₂) is (c) 2 (d) 3 V

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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: linear algebra problem

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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 =…

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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: 5 1 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = -7 3 Ex: 5 ||

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

A: Given: The given vectors are v1=1  1  0  -1: v2=0  1  2  1: v3=1  0  1  -1: v4=1  1  -6  -3: v5=-1…

Q: ii) Two subspaces of R3 are U = {(x,y, z) : x – 3y – 2z = 0} and W = %3D {(r, y, z) : x – y = 0}.…

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Q: Find bases for the four fundamental subspaces of the matrix A. 189 A = 0 30 N(A)-basis N(AT) = %3D…

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Q: -3 Given v = -6 find the coordinates for v in the subspace W spanned by -7 -4 -1 2 3 -2 1 U2 = 1 ,…

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Q: 16 13 Given v = 59 find the coordinates for v in the subspace W spanned by -2 -2 -3 -1 -2 u1 = - u2…

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Q: Q-3 (a) Suppose U = {(x, y, x+y, x- y, 2x) E F5 : x,y E F} Find a subspace W of F5, such that F5 =…

A: U=x,y,x+y,x-y,2x∈F5 : x,y∈ F U=span1,0,1,1,2,(0,1,1,-1,0) We have to find a subspace W of F5 such…

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: -8 Given v = -7 find the coordinates for v in the subspace W spanned by -1 4 -3 u1 3 , U2 and U3 -17…

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Q: -5 6 Given v -8 ind the coordinates for v in the subspace W spanned by -7 -4 2 3 -2 1 Uz 5 Uz -1 and…

A: Step:-1 Given that  v=-5614-8 and u1=021-11,   u2=-735165,  u3=00-101  and  u4=-4-21-21 And u1, u2,…

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: 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: Question 1. Let U be a subspace of R5 of dimension 2. What is the value of dim U-? 3 Other

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

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

A: Subspace W is spanned by the set of vectors v1, v2, v3, v4,v5. Let us try to find are they linearly…

Q: 2 Find the dimension of the subspace H of R spanned by – 12 8 ..... dim H =

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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: 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: 3 and y the Gram-Schmidt process to determine an orthonormal basis for the subspace o

A: Introduction: The formula of the Gram-Schmidt orthogonalization process is given by,…

Q: wont voy work QUESTION #10 CONTINUED b. Is the set of matrices of the form (a) a subspace of M22?

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Q: (5) Suppose that T E L(V) is such that all subspaces of V of dimension dim(V) – 1 are T-invariant.…

A: Please check step 2 for the solution.!

Q: 49. Let A be a fixed n x n matrix and let S = {B e Mnxn | AB = BA} %3D Is S a subspace? Explain.

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.