Use the Gram-Schmidt orthonormalization process to transform the given basis for R? into an orthonormal basis. Use the dot product on R?and use the vectors in the order in which they are given. B = {(1,2) , (–1,0)} o{1, 2), (-승, 음)} o {(* 2 2 O {(-1,0). (0, 1)} O {(-1,0) , (0, 2)}

Q: show two nonzero vectors a and b in the 5th dimensions. put them in vector form and in basis form.…

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Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: Following definition of orthogonal and orthonormal vectors, we find these solutions.

Q: Find the conjugate of z = u+w If u = 6+2i,z= 1+4i

A: Step 1: The conjugate of a complex number z=a+bi is: zˉ=a−bi i.e., it is obtained by changing the…

Q: Is this orthonormal or just orthogonal? I thought you needed to normalize the vectors (i.e. divide…

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Q: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

Q: "Write x as the sum of two vectors, one in Span (u,.u₂.3), and one in Span (U4). Assume that (u) is…

A: In this question , we will write the 'x' as linear combination of remaining vectors .

Q: Which of the following cannot be defined as an inner product between two vectors (x0, Yo) and (¤1,…

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Q: Evaluate the Dot Product u * (v + w). If : u = (-5, 7) v = (1, 6) w = (-11, 2)

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Q: Verify that the vectors (1,0,1), (1,1,-1), es= e₂ = form an orthonormal basis (ONB), and compute the…

A: Given vectors are  .We have to show that these form a orthonormal basis for inner product space…

Q: Determine whether the following vectors are: -1/√√3 1 1/√3 0 1/√√3 2/3 - 1/3 0 - 1/3 Orthogonal but…

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Q: The vectors v1, v2 and v3 form an orthonormal basis for R3 where v1:=vector([0,0,-1]);…

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Q: Let a= and b= Show that there are scalars s and t so that sa+tb=. s = ? t = ?

A: a=-5,0,-3 and b=4,0,2sa+tb=27,0,15

Q: Find the matrix of the standard inner product on W (obtained by restriction of the dot product on…

A: “Since you have asked multiple questions, we will solve the first question specified by you i.e.…

Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

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Q: For vectors, v0= (0,3,4,2),v1= (1,1,2,1), v2= (1,0,0,0), v3= (0,0,1,0), find an orthonormal basis,…

A: Solution by using Gram Schmidt process as follows :

Q: Find the change-of-coordinate matrix P from B to C and P from C to B for the bases B = {1,t,t^2} and…

A: Let U={u1,u2,⋯,un} and V={v1,v2,⋯,vn} are two bases of a vector space W.The identity map I:W→W…

Q: The coordinate vector of the (-4,3,1) in the B={u= (1,1,1); v = (1,0,1); w=(0,0,1)} is : A. (-4,3,1)…

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Q: Find the coordinate vector of a = [*]B= -10-30- 2 with respect to the basis B = for R³.

A: Given: It is given that, x→=42-4 and B=152, 01-6, 001. To find: We have to find the coordinate…

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Q: Multiply the matrix P = A(ATA)-¹AT by itself. Cancel to prove that P² = P. Explain why P(Pb) always…

A: Here the Matrix . For this matrix P, .

Q: For the vectors à = (1, 0, −4) and ¯` = (5, 2, 1) what is the scalar a projection of onto a 1/17 √17…

A: The vectors are given by÷

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Q: Consider the vectors ā₁ = (-1,2,2), a2 = (2,2, -1), and 3 = (2,-1,2). 1. Compute the projection…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

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Q: Find an orthonormal basis of the plane x₁ +4x2x3 = 0.

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Q: Compute the dot product (7, 6, 8) - (4, 10, 8).

A: To find - Compute the dot product 7, 6, 8·4, 10, 8

Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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