Show that {u,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the u's. 2 1 u1 - 3 = "n 2 and x = - 2 %3D U3 - 1 4 1

Q: 5. Let ū = (0,2, 1), ở = (-1,0, 2) and w = (2,3,0). Find the coordinates of (2,2,2) with respect to…

A: This question is related to vector space. Solve in 2nd step .

Q: Show that {₁, ₂} or {₁, ₂, 3) is an orthogonal basis for R² or R³. Find the coordinate of with…

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Q: et B = · 9, (x − 1)², 3x³) be an ordered basis for P3. Find the coordinate vector of (x) = 3x³ + 2x²…

A: Coordinate vector

Q: - Linear maps Consider the following three vectors in R³: 1 0 --0) --(9)· --0 V1 = 1 V3 = = -1 1 (a)…

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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: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

Q: . Determine if the vectors (3,2,0) , (-3,0,1) , and (1,1,–9) span all of R’ . Do these vectors form…

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Q: Find an orthonormal basis of the plane ¤1 + 5x2 – x3 = 0. %3D

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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 an orthogonal basis for A1, A2, A3 (i.e., find 3 mutually perpendicular vectors u1, u2, u3 with…

A: The solution are next step

Q: Find the basis for the orthogonal complement V: v1=(1,-3,3,5) v2=(2,-5,9,3)

A: The given vectors  and .The objective is to find the orthogonal complement of the given vectors.

Q: Please don't provide handwritten solution ....

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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: Suppose {u, } form an orthogonal basis in R2 and y = 2ū - 7 where u = (8) 6 If W = Span{}, what is…

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Q: Let e1, e2, e3, e4, ē5, e6} be the standard basis in R°. Find the length of the vector * = 471+…

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Q: Find the stable vector of 0 0 1 1 P 2 1 3 3 ..-

A: It is an important part of statistics. It is widely used.

Q: Let {u₁, U₂, U3, U4} be the orthogonal basis for R¹ given below. Write x as a sum of two vectors v₁…

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