Let S be a subspace of R with basis B={[0,1,-3], [3,3,0]) The coordinate vector of v=[-15,-20,15] with respect to is [= %3D
Q: (2) Find a basis for the subspace W = {(a +c, 2a – b, 3a – 26 – c,b+ 2c) | a, b, c € R} of R.
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- Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). 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.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.Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
- Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.