Question number 16 please !

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 number 16 please !

 

a1l
a12 a13
13. Let T = {
a21
M2x3(R) : aii + a12 + ai13 = A31 + a22 + a23
a22
A23
0}.
0 -1
0 0
1 -1
0 0 0
) 0 0
0 0 0
0 1
Verify that B =
is a
1 0
basis for T.
In exercises 14-19 determine if the sequence B' is a basis for the space T of exercise
13.
See Method (5.3.2). Note that if there are the right number of vectors you still have to
show that the vectors belong to the subspace S.
-1
).
14. B'
%3D
0
1
-1
-1
1
-2
1
00 0
1
15. B' =
-
0 0
-1 0
1))"
1
1
-2
-1
(G
().
-1
1 -2
0 0 0
16. B'
1
1
2 -3
-1 0
1
0 0
Transcribed Image Text:a1l a12 a13 13. Let T = { a21 M2x3(R) : aii + a12 + ai13 = A31 + a22 + a23 a22 A23 0}. 0 -1 0 0 1 -1 0 0 0 ) 0 0 0 0 0 0 1 Verify that B = is a 1 0 basis for T. In exercises 14-19 determine if the sequence B' is a basis for the space T of exercise 13. See Method (5.3.2). Note that if there are the right number of vectors you still have to show that the vectors belong to the subspace S. -1 ). 14. B' %3D 0 1 -1 -1 1 -2 1 00 0 1 15. B' = - 0 0 -1 0 1))" 1 1 -2 -1 (G (). -1 1 -2 0 0 0 16. B' 1 1 2 -3 -1 0 1 0 0
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