Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below. 1 2 -4 3 2 1 2 -4 3 5 10 - 9 -7 3 0 0 1 - 2 A = 8 -9 -2 1 0 0 0 -7 -2 - 4 0 - 4 0 0 A basis for Col A is given by O- (Use a comma to separate vectors as needed.) The dimension of Col A is A basis for Nul A is given by O. (Use a comma to separate vectors as needed.) The dimension of Nul A is 2.

Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below. 1 2 -4 3 2 1 2 -4 3 5 10 - 9 -7 3 0 0 1 - 2 A = 8 -9 -2 1 0 0 0 -7 -2 - 4 0 - 4 0 0 A basis for Col A is given by O- (Use a comma to separate vectors as needed.) The dimension of Col A is A basis for Nul A is given by O. (Use a comma to separate vectors as needed.) The dimension of Nul A is 2.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 41CR: 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...

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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 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.
Find an orthonormal basis for the solution space of the homogeneous system of linear equations. x+yz+w=02xy+z+2w=0