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Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 16CM

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Question

Find the value of a.

Find the value of b.

Find the value of b.

Find the value of d.

14
After applying the Gram-Schmidt Orthonormalization Process to the basis B =
16
a
we get the basis B'
d

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Use the inner product u,v=2u1v1+u2v2 in R2 and Gram-Schmidt orthonormalization process to transform {(2,1),(2,10)} into an orthonormal basis.
Find a basis for R2 that includes the vector (2,2).
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Use the Gram-Schmidt orthonormalization process to find an orthogonal matrix P such that PTAP diagonalizes the symmetric matrix A=[022202220].
Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
2. Find an orthonormal basis by the Gram-Schmidt procedure for the basis (-4,1) and (3,7)
Apply Gram - Schmidt process to construct an orthonormal for R4 with the standard inner product from the basis (V1, V2, V3) where V, = (1, 1, 1, 1), V2 = (1, 2, 0, 1), V3 = (2, 2, 4, 0).
Apply the Gram-Schmidt process to obtain an orthonormal basis for the 51 space spanned by the vectors 4 6 Show your work.
Use the Gram-Schmidtorthonormalization process to find an orthonormal basis of ?2(with the dot product)from the basisthe basis{(4,−3,0),(1,2,0),(0,0,4)}.
Apply the Gram-Schmidt orthonormalization process to transform the given basis for R" into an orthonormal basis. Use the vectors in the order in which they are given. B = {(15, 8), (1, 0)} uj = Uz =
Apply the Gram-Schmidt orthonormalization process to transform the given basis for R" into an orthonormal basis. Use the vectors in the order in which they are given. {(0, 1), (3, 6)} u1 = u2 =
Apply tion procesS the Gram-Schmidt orthonormaliza- to transform the basis B = {(1, 1,0, 1), (1, –2,0,0), (1,0, –1, 2)} for R4 standard inner product into an orthonormal basis. with -

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