Find the bases for the row space and column space of the matrix 1 -2 5 0 3 5 -7 0 -6 3 -2 1 -3 8 -9 1 -9, A -2 −1 -3 consisting entirely of row vectors, or column vectors, from A. What are the rank and mullity of the matrix? Hint: You can use the RREF of A to find a basis of the column space. However, to find a basis of the row space of A consisting entirely of row vectors of A, you need to use the RREF of AT. For instance, let B - (1²) 2 2 12

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The RREF of B is
6)
but the first two rows of B is not the basis for row(B). On the other hand, the RREF
of BT is
1 2
(639)
00
the first and the third rows of B form a basis for row(B).
B =
Transcribed Image Text:The RREF of B is 6) but the first two rows of B is not the basis for row(B). On the other hand, the RREF of BT is 1 2 (639) 00 the first and the third rows of B form a basis for row(B). B =
Find the bases for the row space and column space of the matrix
-2 5 0 3
5
-7 0
-6
3
-2 1 -3
-3 8
-9 1-9
A =
1
-2
consisting entirely of row vectors, or column vectors, from A. What are the rank and
nullity of the matrix?
Hint: You can use the RREF of A to find a basis of the column space. However, to
find a basis of the row space of A consisting entirely of row vectors of A, you need to
use the RREF of AT. For instance, let
-(1)
2 2
2
B =
Transcribed Image Text:Find the bases for the row space and column space of the matrix -2 5 0 3 5 -7 0 -6 3 -2 1 -3 -3 8 -9 1-9 A = 1 -2 consisting entirely of row vectors, or column vectors, from A. What are the rank and nullity of the matrix? Hint: You can use the RREF of A to find a basis of the column space. However, to find a basis of the row space of A consisting entirely of row vectors of A, you need to use the RREF of AT. For instance, let -(1) 2 2 2 B =
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