Use the fact that matrices A and B are row-equivalent. 1 2 1 2 5 1 1 A = 3 7 2 2 -2 6 13 5 -1 [10 30 -4 0 1 -1 0 0 0 0 1 -2 0 0 4 2 B = 0 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. (d) Find a basis for the column space of A. (e) Determine whether or not the rows of A are linearly independent. O independent O dependent (f) Let the columns of A be denoted by a1, a2, a3, a4, and as. Which of the following sets is (are) linearly independent? (Select all that apply.) O {a,, a2, a4} O {a,, a2, a3} O {a1, a3, as} I 1

Use the fact that matrices A and B are row-equivalent. 1 2 1 2 5 1 1 A = 3 7 2 2 -2 6 13 5 -1 [10 30 -4 0 1 -1 0 0 0 0 1 -2 0 0 4 2 B = 0 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. (d) Find a basis for the column space of A. (e) Determine whether or not the rows of A are linearly independent. O independent O dependent (f) Let the columns of A be denoted by a1, a2, a3, a4, and as. Which of the following sets is (are) linearly independent? (Select all that apply.) O {a,, a2, a4} O {a,, a2, a3} O {a1, a3, as} I 1

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 18CM

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