Determine if y is in the subspace of R* spanned by the columns of A. -5 18 -6 -8 -9 29 5 -5 A= 4. 6 -9 9-3 -7 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The vector y is in the subspace spanned by the columns of A because y can be written as a linear combination of these columns as follows. - 5 18 -6 -8 29 -5 y%3= %3D 4. 6. -9 4. 9 (Type integers or simplified fractions.) O B. The vector y is not in the subspace spanned by the columns of A.

Determine if y is in the subspace of R* spanned by the columns of A. -5 18 -6 -8 -9 29 5 -5 A= 4. 6 -9 9-3 -7 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The vector y is in the subspace spanned by the columns of A because y can be written as a linear combination of these columns as follows. - 5 18 -6 -8 29 -5 y%3= %3D 4. 6. -9 4. 9 (Type integers or simplified fractions.) O B. The vector y is not in the subspace spanned by the columns of A.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 73CR

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Similar questions

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?
Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
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.
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.
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
Spanning the Same Subspace In Exercises 61and 62, show that the sets S1and S2span the same subspace of R3. S1={(0,0,1),(0,1,1),(2,1,1)} S2={(1,1,1),(1,1,2),(2,1,1)}
Proof Prove that if S1 and S2 are orthogonal subspaces of Rn, then their intersection consists of only the zero vector.