3 A = 3 3 -20 4 3 -5-2-9 -6 -6 4 6 22 (a) Find the dimension of the row space of A and a basis for the row space of A. [1 1 0 0 2] RREF(A)= 0 0 1 0 1 00015 (b) Find the dimension of the column space of A and a basis for the column space of A. (c) Find the dimension of null(A) and a basis for null(A). (d) The Rank-Nullity Theorem says that for any m x n matrix A n = dim(null(A)) + dim(Im(A)).
3 A = 3 3 -20 4 3 -5-2-9 -6 -6 4 6 22 (a) Find the dimension of the row space of A and a basis for the row space of A. [1 1 0 0 2] RREF(A)= 0 0 1 0 1 00015 (b) Find the dimension of the column space of A and a basis for the column space of A. (c) Find the dimension of null(A) and a basis for null(A). (d) The Rank-Nullity Theorem says that for any m x n matrix A n = dim(null(A)) + dim(Im(A)).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![[1 1 0 0 2]
0 0 1 0 1
[00015]
(a) Find the dimension of the row space of A and a basis for the row space of A.
A =
3
3
-2 0 4
3
3 -5 -2 -9
-6 -6 4 6 22
RREF(A)
=
(b) Find the dimension of the column space of A and a basis for the column space of A.
(c) Find the dimension of null(A) and a basis for null(A).
(d) The Rank-Nullity Theorem says that for any m x n matrix A
n= dim(null(A)) + dim(Im(A)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4f4b624-9180-41b5-94fa-c093ec7455d7%2Fd892cce1-5987-4162-9b63-c0cc94d27caa%2Fjk85skp_processed.png&w=3840&q=75)
Transcribed Image Text:[1 1 0 0 2]
0 0 1 0 1
[00015]
(a) Find the dimension of the row space of A and a basis for the row space of A.
A =
3
3
-2 0 4
3
3 -5 -2 -9
-6 -6 4 6 22
RREF(A)
=
(b) Find the dimension of the column space of A and a basis for the column space of A.
(c) Find the dimension of null(A) and a basis for null(A).
(d) The Rank-Nullity Theorem says that for any m x n matrix A
n= dim(null(A)) + dim(Im(A)).
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