(a) Let A be a nonzero 6 × 9 matrix. Explain your answer. (i) What is the largest possible dimension of Col(A)? What is the smallest possible nullity(A)? (ii) Find nullity(A) if Col(A) = R6. (b) Suppose that a 5 × 8 matrix A has rank 3. Find nullity(A) and dim Row(A).

(a) Let A be a nonzero 6 × 9 matrix. Explain your answer. (i) What is the largest possible dimension of Col(A)? What is the smallest possible nullity(A)? (ii) Find nullity(A) if Col(A) = R6. (b) Suppose that a 5 × 8 matrix A has rank 3. Find nullity(A) and dim Row(A).

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 64E

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Question

(a) Let A be a nonzero 6 × 9 matrix. Explain your answer.
(i) What is the largest possible dimension of Col(A)? What is the smallest possible nullity(A)?
(ii) Find nullity(A) if Col(A) = R6.
(b) Suppose that a 5 × 8 matrix A has rank 3. Find nullity(A) and dim Row(A).

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