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Let A be an m xn matrix over R. We define NA := {x € R" : Ax = 0}. Na is called the kernel of A and v(A) := dim(Na) is called the nullity of A. If NA only contains the zero vector, then v(A) = 0. (i) Let %3D 1 A = 2 -1 Find NA and v(A). (ii) Let -1 3 A = 4 -2 -6 3 -9 Find NA and v(A).

Let A be an m xn matrix over R. We define NA := {x € R" : Ax = 0}. Na is called the kernel of A and v(A) := dim(Na) is called the nullity of A. If NA only contains the zero vector, then v(A) = 0. (i) Let %3D 1 A = 2 -1 Find NA and v(A). (ii) Let -1 3 A = 4 -2 -6 3 -9 Find NA and v(A).

Elementary Linear Algebra (MindTap Course List)
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 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...
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Let A be an m x n matrix over R. We define NA := {x € R" : Ax = 0}. Na is called the kernel of A and v(A) := dim(Na) is called the nullity of A. If NA only contains the zero vector, then v(A) = 0. (i) Let %3D 1 A = 2 -1 Find NA and v(A). (ii) Let -1 3 A = -2 -6 3 -9 Find NA and v(A).
Transcribed Image Text:Let A be an m x n matrix over R. We define NA := {x € R" : Ax = 0}. Na is called the kernel of A and v(A) := dim(Na) is called the nullity of A. If NA only contains the zero vector, then v(A) = 0. (i) Let %3D 1 A = 2 -1 Find NA and v(A). (ii) Let -1 3 A = -2 -6 3 -9 Find NA and v(A).
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