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

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 23EQ

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Question

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

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