2. Consider the subspace im(A) of Rº, where 1 1 A = | 1 1 3 Find a basis of ker(A"), and draw a sketch illustrating the formula (im A)- = ker(A?) in this case. T

Q: (2) Find a basis for the subspace W = {(a +c, 2a – b, 3a – 26 – c,b+ 2c) | a, b, c € R} of R.

A: We need to find the basis for the given subspace:

Q: (2) Find a basis for the subspace W = {(a+c,2a – 6, 3a – 26 – c, b + 2c) | a, b, c E R} of R4

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Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. -1 4 4 1 S = = span 1 6.

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Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. 3 S = span 4

A: In this question, we find the orthogonal set of basis by the Gram-Schmidt process.

Q: Given the basis {x,, X, cohere X,= 「に XgJ for R3 2 3. use the Gram - Schmidt process tO transform…

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Q: 4. Find an orthogonal basis of the subspace W of R5 spanned by {ū₁ = (1, 1, 1, 0, 1), 2 = (1, 0, 0,…

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Q: Find a basis of the subspace of Rª defined by the equation 6x1 9x2 + 2x3 + 5x4 = 0 { Basis:

A: NOTE: Refresh your page if you can't see any equations. . divide both sides by 6

Q: 2) Let W be a subspace of V = Rª with basis 1 1 1 V,ミ V3 1 Using Gram Schmidt process, find the…

A: The vector of the sub-space are,

Q: Given the basis B for a subspace W of R3. Use the alternative form of the Gram-Schmidt process to…

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Q: 2. Find a basis and the dimension of the subspace W = {(0,a+b,a-b); a,be R}

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Q: Let [1 37 A = 2 4 Find an orthonormal basis of the image of A.

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

A: The solution is given as

Q: 1. Consider the vector space V = M3x3(C) ôver the neld all matrices of the form 211 Z33 Find a basis…

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Q: Consider the vectors 7₁ = €₂ = T3 = 1 in R4. Use the Gram-Schmidt process to find an orthogonal…

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Q: 7 4. 3 and let W the subspace of IR spanned by u and v. Find a basis of W, the orthogonal complement…

A: The objective is to find orthogonal complement of W

Q: 1) Interpolate (by hand) the data x = [-1,0,1] %3D y = [0,1,3] using a) the linear spline basis;

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Q: The given vectors form a basis for a subspace W of R3 or R4. Apply the Gram-Schmidt Process to…

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Q: 1. The given vectors form a basis of a subspace of R°. Use Gram-Schmidt process to obtain an…

A: In this problem, the Gram Schmidt process is used to solve the question

Q: Explain how fixing a basis v1, corresponding function in n variables of the form q(x1, · ·· , Xn) =…

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Q: The Gram-Schmidt process transforms the basis u,=(1, 3), u,=(1, –7) of R² into the orthogonal basis…

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Q: 3 Find a basis of the subspace of R' defined by the equation -7x1 – 5x2 – 4x3 = 0.

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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: 1 2 Find a basis for subspace V of R4 spanned by the vectors 3 dimension of V? 8 What is the

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Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. -3° 2 , 83 = S2 1

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Q: 8. Q4) Let 5 } is a basis for a subspace W. Use the Gram-Schmidt prosses to produce an orthogonal…

A: Here, let v1=30-1, v2=85-6 are the basis element for a subspace of W.

Q: Find a basis for the subspace a W = E R2x2 | 6a + 2b – c = d of R2x2- A basis for W is 1 0 0 Ex: 1 :

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Q: Find a basis for the following subspace of Rª over R: 3 1 4 7 span 10 11 13 What is the dimension of…

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Q: 3) li) Find the dual basis {l, l} of the standard basis of IR". (i) Fiod th

A: Since you have asked more than one question, we will solve first one for you. If you want other…

Q: {[:} 5. (a) Consider the subspace W = span and consider the vector -1 1 u = -1 |. Find the vector w…

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Q: Find a basis for the subspace 96 4a + 6b W = E R2x2 a, b eR} of R2x2- 86 5a Ex: 1 4 6. A basis for W…

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Q: 2. Consider the quadratic form Q : R° → R, where Q(x1, 22, x3) = –2x – 8x – 18x3+ 8x1x2 + 4x1x3 +…

A: The given quadratic form is Q(x1,x2,x3)=-2x12-8x22-18x32+8x1x2+4x1x3+4x2x3 The quadratic homogenous…

Q: Consider the matrix -1 A = 1 1 Find a basis of the orthogonal complement of the null space of A. ||

A: We know that Null Space of A={ x∈ℝ2 : Ax=0 }where x=( x1 , x2 )Orthogonal complement of vector  x=(…

Q: Let A = -1 -9 3

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Q: 3 Find a basis of the subspace of R’ defined by the equation -5x1 – 7x2 – 2x3 = 0.

A: Consider the given equation:

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

A: Given data÷

Q: 3. In the space of square matrix M2x2 find representation of vector A = L4 from the basis U1 ; Uz =

A: As basis is given . So, vector A can be written as linear combination of basis vectors .

Q: Find a basis of a subspace U in R given by a system: I1 - T2 + 2r3+T1 T1- 12 + 313 + 2r, 0

A: (a) Given the system x1-x2+2x3+x4=0x1-x2+3x3+2x4=0 which describes the subspace U∈ℝ4.   To find 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: Use Gram-Schmidt to find an orthogonal basis for R' if B={(2, -5), (1, 3)}.

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Q: The set of S = {x1 = |0,x3 = 1 is based on R^3. Using the wwww www. www Gram-Schmidt method, obtain…

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Q: 2. The set of vectors orthogonal basis for W. 30 CT 00 5 is a basis for a subspace W. Use the…

A: The set of vectors 30-1,85-6 is a basis for a subspace W.

Q: Use Gram-Schmidt to find an orthogonal basis for R if B={(-5, 2), (3, -1)}.

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Q: Find a basis and the dimensi on of the subspace W of V = M22 spanned by A B

A: V=M2X2R SPANNED BY A=1-5-42, B=11-15, C=2-4-57, D=1-7-51 Solution:- To find: A basis and the…

Q: 4. (a) Find a basis for the subspace H of R spanned by the following vectors: 00000 1 (b) What is…

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Q: If By = {v1, v2, ..., Vn} is a basis for V, show that there exist n +1 nested subspaces of V.

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Q: 4. Consider the subspace V of R' given by 1 3 V = span (a) Find an orthonormal basis for the…

A: Solution:-

Q: Suppose a matrix A has singular value decomposition A = UEVT, 0 0 300 0 2 0 0 0 1 where U = 1 0. 0.…

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Q: Let H be the subspace of R' described by 51-3r2-4x3 = 0. Find a basis B for HCR. Give your answer as…

A: In the given problem we we have to find the basis of H which is a subspace of R4. so every element…

Q: se 3 Find a basis of the null space N(A) C R of the matrix 1. -2 A = -3 E M3x5(R) 6 -1 -7 -4 5 8 -4…

A: