(5) Let A be an mxn matrix. The row space of A, denoted rowspace(A), is the span of the row vectors of A. Since row operations are nothing more than linear combinations of the row vectors, we see that if A and B are two row-equivalent matrices, then rowspace(A)=rowspace(B). Therefore, the set of nonzero row vectors in any row- echelon form of an m x n matrix A is a basis for rowspace(A). (a) Suppose the following 4 x 6 matrix A has been row reduced accordingly: 14-15 4 -1 2 3 5 5-5-6-9 6 -6 -6 -8 2 1 3 0 A= 1 -2-7 -2-6 1 5 -> Row space • Determine the dimension of the row space of A 01 30 00 00 • Determine a basis for the row space of A • Determine the vector space that contains the row space of A Column space • Determine the dimension of the column space of A 10 01 • Determine the vector space that contains the column space of A • Determine a basis for the column space of A Null space • Determine the dimension of the nullspace of A • Determine a basis for the nullspace of A • Determine the vector space that contains the nullspace of A
(5) Let A be an mxn matrix. The row space of A, denoted rowspace(A), is the span of the row vectors of A. Since row operations are nothing more than linear combinations of the row vectors, we see that if A and B are two row-equivalent matrices, then rowspace(A)=rowspace(B). Therefore, the set of nonzero row vectors in any row- echelon form of an m x n matrix A is a basis for rowspace(A). (a) Suppose the following 4 x 6 matrix A has been row reduced accordingly: 14-15 4 -1 2 3 5 5-5-6-9 6 -6 -6 -8 2 1 3 0 A= 1 -2-7 -2-6 1 5 -> Row space • Determine the dimension of the row space of A 01 30 00 00 • Determine a basis for the row space of A • Determine the vector space that contains the row space of A Column space • Determine the dimension of the column space of A 10 01 • Determine the vector space that contains the column space of A • Determine a basis for the column space of A Null space • Determine the dimension of the nullspace of A • Determine a basis for the nullspace of A • Determine the vector space that contains the nullspace of A
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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Transcribed Image Text:(5) Let A be an mxn matrix. The row space of A, denoted rowspace(4), is the span of the
row vectors of A. Since row operations are nothing more than linear combinations
of the row vectors, we see that if A and B are two row-equivalent matrices, then
rowspace(4)=rowspace(B). Therefore, the set of nonzero row vectors in any row-
echelon form of an m x n matrix A is a basis for rowspace(A).
(a) Suppose the following 4 x 6 matrix A has been row reduced accordingly:
14-15
A =
1 4-1 2 3 5
-2 -7
-2-6
5 -5 -6 -9
6 -6 -6 -8
1
1 3 0
5 2
→
Row space
• Determine the dimension of the row space of A
01 30
00 10
00
0 1
• Determine the vector space that contains the row space of A
. Determine a basis for the row space of A
Column space
• Determine the dimension of the column space of A
• Determine the vector space that contains the column space of A
• Determine a basis for the column space of A
Null space
• Determine the dimension of the nullspace of A
• Determine the vector space that contains the nullspace of A
• Determine a basis for the nullspace of A
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