5. Find basis for the subspace u- of R for the vector u (1,3, -4). (Here u- means %3D orthogonal subsnace of u)

Q: 5. Show that if H and H2 are two orthogonal subspaces of H, then Hin H2 = {0}. Does the converse…

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Q: Suppose U and W are subspaces of V such that dimU=4, dimW=5, and dimV=7. Find the possible…

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Q: 個同 . Find a basis for the Subspace W of R spanned by S What is the dimension of W?

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Q: Find a basis for the subspace of R3 spanned by s. S = {(1, 5, 9), (-1, 6, 9), (2, 6, 1)}

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Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 2, 6), (-1, 3, 6), (2, 3, 1)}

A: The given subspace is: S= (1, 2, 6), (-1, 3, 6), (2, 3, 1)

Q: Find a basis for the subspace of R3 spanned by S.S = {(4, 4, 8), (1, 1, 2), (1, 1, 1)}

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Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = -197 1 -13 10 5 8-6…

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Q: in R3, find the orthogonal projection matrix on the subspace defined by the equation: 2x-y- 3z = 0.…

A: Given:- Equation 2x-y-3z=0 and to be found the orthogonal projection matrix.

Q: Prove that the subspaces of R3 are {0}, R3 itself, and any line or plane passing through the origin.

A: Let S be a subspace for R3   Hence,              If S is the subspace then by definition:…

Q: 16 In the vector space R, let u= (1, 2, 3), v -(3, 1, 5), w-(3,-4, 7). Prove that the subspace S…

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Q: 3.8 Using the Gram-Schmidt method, turn the basis B = (b1, b2) of a two- dimensional subspace U C R…

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Q: Criticize the following argument: For any vector v, we have Ov = 0. So the first criterion for…

A: Let W be the subset of a vector space V. If W is itself a vector space under the operations of V,…

Q: Suppose V is finite-dimensional and U and W are subspaces of V with W^0 ⊂ U^0. Prove that U ⊂ W.

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Q: (3) Suppose that V is a finite dimensional vector space over R and T € L(V) has no eigenvalues.…

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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: Let S be a subspace of V. Starting with a basis {81,..., s} for S, how would you find a basis for…

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Q: Find a basis for the subspace of R, the plane 2x +y-z+ 3w-0 and convert it into an orthonormal ban

A: Given the subspace 2x+y-z+3w=0. To get the orthonormal basis. The formula for orthonormal basis is,…

Q: ind the closest point in the subspace with the (not orthogonal) basis {b1, b2, b3} to the head of…

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Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 4, 7), (-1, 5, 7), (2, 5, 1)}

A: The matrix form the vectors is: A=1-12455771

Q: Suppose {x,y} is a basis for a subspace W of Rn. Let u = x + y and v = x − y. Show that {u,v} is…

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Q: Find a basis for the subspace of R3 spanned by S. S = {(5, 9, 9), (1, 2, 2), (1, 1, 1)}

A: To find the basis for the subspace of R3 spanned by the given set of vectors S.

Q: 4. Find an orthonormal basis for W+, where W is the subspace of R' spanned by the vectors (-1,…

A: To find- Find an orthonormal basis for W⊥, where W is the subspace of ℝ4 spanned by the vectors -1,…

Q: 1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

A: Solution:-

Q: 9. Find a basis for the orthogonal complement of the subspace W=Span

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Q: 16 In the vector space R, let u= (1, 2, 3), v = (3, 1, 5). w = (3,-4, 7). Prove that the subspace S…

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Q: 2. Prove that the set S is a subspace of the vector space V.(5 V = R3x3 and S is the set of upper…

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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: Find a basis for the subspace of R3 spanned by S. S = {(1, 3, 6), (-1, 4, 6), (2, 4, 1)} EEE

A: Basis of subspace of ℝ3 i) It must be linearly independent. ii) Its span ℝ3

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

A: Given data÷

Q: If W is a subspace of ℝ4 whose dimension is 2 then is any set of 2 vector is a basis for W

A: Answer

Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0, 3), (2, 1, –2), (0, – 1, 8),…

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Q: Is the following set of vectors in R 3 linearly dependent: {(1, 0, 3),(2, 1, -2),(0, -1, 8),(7, 2,…

A: The solution is given as

Q: Find a basis for the subspace W of R spanned by 3 7 2 2 10 6. 7 4 What is the dimension of W?

A: Given vectors, 122, 321, 11107, 764

Q: If x is in W, then x is orthogonal to some vector in a subspace W

A: SOLUTION-

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: 9

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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: If W is a subspace of R" and if u is in both W and w then u must be a zero vector.

A: I am going to solve the given problem by using the orthogonal property of a vector.

Q: If Pa is the Vector Space of poly romiels Of degee ss and Be is tho kctor of Spaco Of purynomals of…

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Q: (2) Find a basis for the subspace W%3D { (а+c, 2a — b, За — 2b — с, b + 2с) | а, b, с € R} of R4.

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Q: Show that an arbitrary linear combination of two states Vs in the vector space V with the same…

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Q: Find the orthogonal projection of onto the subspace W of Rª spanned by projw() = v= 4 -2 -13] 3 15…

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Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0,3), (2, 1, –2), (0, – 1,8), (7,2,…

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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: Let u, = u2 = -1. and uz =0| Note that u, and uz are orthogonal but that uz is not orthogonal to…

A: Introduction: If two vectors are perpendicular to one other, they are said to be orthogonal. The dot…

Q: Let W be the subspace of R3 with orthonormal basis {w1, w2}, where

A: Given: w1=010 w2=15025 v=12-1

Q: Let T: V-->W be a linear transforma­tion between finite-dimensional vector spaces V and W Let B…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Find the orthogonal projection of onto the subspace W of Rª spanned by 1 projw (v)

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Q: 2. Let U and W be a subspaces of an n-dimensional vector space V and suppose further that UNW={0}…

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Q: 2. Let S = {vi, v2, V3} be a set of linearly dependent vectors in an inner product space V. What is…

A: To explain: What will be the result when we apply Gram-Schmidt process to a linearly dependent set…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.