7. Rank and Nullity: 1 2 1 Let A - 2 4 2 a) Find the rank of matrix A. 3 6 3 b) Find the nullity of matrix A. c) Show that the rank-nullity theorem holds for matrix A. 8. Change of Basis: Consider the vector space R² with the standard basis {e1 = (1,0), e2 = (0, 1)} and a new basis {v1 = (1, 1), V2 = (1, −1)}. a) Find the change of basis matrix from the standard basis to the new basis. b) Express the vector w = (2, 3) in the new basis {V1, V2}.

7. Rank and Nullity: 1 2 1 Let A - 2 4 2 a) Find the rank of matrix A. 3 6 3 b) Find the nullity of matrix A. c) Show that the rank-nullity theorem holds for matrix A. 8. Change of Basis: Consider the vector space R² with the standard basis {e1 = (1,0), e2 = (0, 1)} and a new basis {v1 = (1, 1), V2 = (1, −1)}. a) Find the change of basis matrix from the standard basis to the new basis. b) Express the vector w = (2, 3) in the new basis {V1, V2}.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 69E: Find a basis for R2 that includes the vector (2,2).

See similar textbooks