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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 1 A = 2 -1 3 Find NA and v(A). (ii) Let 2 -1 3 A = 4 -2 6. -6 3 -9 Find NA and v(A).

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 1 A = 2 -1 3 Find NA and v(A). (ii) Let 2 -1 3 A = 4 -2 6. -6 3 -9 Find NA and v(A).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let A be an m x n matrix over R. We define NA := {x € R" : Ax = 0}. dim(NA) is called the nullity of A. If NA is called the kernel of A and v(A) := NA only contains the zero vector, then v(A) = 0. (i) Let 1 A = 2 2 -1 3 Find NA and v(A). (ii) Let 2 -1 3 A = 4 -2 6. -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}. dim(NA) is called the nullity of A. If NA is called the kernel of A and v(A) := NA only contains the zero vector, then v(A) = 0. (i) Let 1 A = 2 2 -1 3 Find NA and v(A). (ii) Let 2 -1 3 A = 4 -2 6. -6 3 -9 Find NA and v(A).
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