CONSIDER THE MATRIx 1 41 2 3 2 22 1IND A BASIS FOR AND THE DIMENSION OF RA IN A BASIS fOR AND THEDIMEN SION OFNA A BASIS fOK AND THE DINeNSION Of RnT NAT 1 L (( ( 17 WHICH OF THE QUANTInes IN (a) - (d) abovc w (are) the Rank CA)? OM 11
CONSIDER THE MATRIx 1 41 2 3 2 22 1IND A BASIS FOR AND THE DIMENSION OF RA IN A BASIS fOR AND THEDIMEN SION OFNA A BASIS fOK AND THE DINeNSION Of RnT NAT 1 L (( ( 17 WHICH OF THE QUANTInes IN (a) - (d) abovc w (are) the Rank CA)? OM 11
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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Question
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please answer 4 & 5. thank you.
![CONSIDER THE MATRIx
1
41
2
3
2
22
1IND A BASIS FOR AND THE DIMENSION OF RA
IN A BASIS fOR AND THEDIMEN SION OFNA
A BASIS fOK AND THE DINeNSION Of RnT
NAT
1 L
((
(
17
WHICH OF THE QUANTInes IN (a) - (d) abovc w (are) the
Rank CA)?
OM
11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a6fbc47-0260-4cf4-8ea3-0a7314648440%2F57288094-9e3a-4ce8-8b38-4c8c48ab1cd0%2F36ysya.jpeg&w=3840&q=75)
Transcribed Image Text:CONSIDER THE MATRIx
1
41
2
3
2
22
1IND A BASIS FOR AND THE DIMENSION OF RA
IN A BASIS fOR AND THEDIMEN SION OFNA
A BASIS fOK AND THE DINeNSION Of RnT
NAT
1 L
((
(
17
WHICH OF THE QUANTInes IN (a) - (d) abovc w (are) the
Rank CA)?
OM
11
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
4.
Compute the transpose as shown below.
![2
4 0 1
AT
1
2 3 2
0 1
2
2 1
0
4 2 0
0 3
1
1
2 2](https://content.bartleby.com/qna-images/answer/9a6fbc47-0260-4cf4-8ea3-0a7314648440/5cba476a-fd16-466b-a14f-3df9e16fed49/xsamh1.png)
Step 2
Obtain the null space for transpose of A as follows.
![2
1
0
0
х
4 20
у
1
0
0 3
0
1
2 2
0
2х + у
0
4x 2y
=0
Зу+2
0
x+ 2y+ 2z
By solving these four equations
x0, y 0 and - 0.
This implies that null space of AT contains only zero element
hence, Requird basis is an empty set and its dimension is zero.](https://content.bartleby.com/qna-images/answer/9a6fbc47-0260-4cf4-8ea3-0a7314648440/5cba476a-fd16-466b-a14f-3df9e16fed49/93vvitk.png)
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