1. A matrix A and its reduced echelon form are given below. [1 0 5/2 -9/2 7/2] 0 1 3/2 -5/2 3/2 0 0 0 0 0 3 -5 0 -1 3 -7 9 -4 9 -11 -5 7 -2 5 3 -7 -3 4 -7 (a) Give integers p and q so that Col(A) is a subspace of RP and Nul(A) is a subspace of R". (b) Give a basis for the column space of A. (c) Give a basis for the null space of A. CONTINUED 1 2. Explain why each set is not a basis for R. (a) (b) (c) (d)

1. A matrix A and its reduced echelon form are given below. [1 0 5/2 -9/2 7/2] 0 1 3/2 -5/2 3/2 0 0 0 0 0 3 -5 0 -1 3 -7 9 -4 9 -11 -5 7 -2 5 3 -7 -3 4 -7 (a) Give integers p and q so that Col(A) is a subspace of RP and Nul(A) is a subspace of R". (b) Give a basis for the column space of A. (c) Give a basis for the null space of A. CONTINUED 1 2. Explain why each set is not a basis for R. (a) (b) (c) (d)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...

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