Let A be an m x n matrix over R. We defineNA := {x € R" : Ax = 0}.dim(NA) is called the nullity of A. IfNA is called the kernel of A and v(A) :=NA only contains the zero vector, then v(A) = 0.(i) Let1A =22 -13Find NA and v(A).(ii) Let2-13A =4-26.-63-9Find NA and v(A).

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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).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 30E

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Question

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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