an(1-1)). Show that R2 = span We must show that for any vector 1 a -1 b ×[1] + »[_1] = [8] for some x, y. Row-reduce the associated augmented matrix: R₁ - R₂ So given a and b, we have + b [] 2 R₂ - R₁ 10 01 we can write 1 1 0-2 2a - b 2 b-a 2 2a - b 2 X a b )[H])+(2 - 12/21 X - 12/22₂22 1 1 0 1 [4]-[8] b-a 2 X X
an(1-1)). Show that R2 = span We must show that for any vector 1 a -1 b ×[1] + »[_1] = [8] for some x, y. Row-reduce the associated augmented matrix: R₁ - R₂ So given a and b, we have + b [] 2 R₂ - R₁ 10 01 we can write 1 1 0-2 2a - b 2 b-a 2 2a - b 2 X a b )[H])+(2 - 12/21 X - 12/22₂22 1 1 0 1 [4]-[8] b-a 2 X X
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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need help
![Show that R2
= span
We must show that for any vector
X
1
(1) (-1)).
1
A+4-8
y
-1
for some x, y. Row-reduce the associated augmented matrix:
1
1
1 -1
a
R₁
+
a
b
So given a and b, we have
b
a
[:]
b
10
- R₂
40
0 1
2
a
>
b
R₂ - R₁
we can write
1 1
0-2
2a - b
2
b-a
2
2a - b
2
X
X
=
1 1
a b
[B]+($- £¸)[4]•B]}]
2 2
-1
b
0 1
b - a
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3cf874b-7a7b-478f-a7b8-421442e72224%2F1cbae844-433e-4ff2-9b03-1a043c6b4557%2Frvmfvjn_processed.png&w=3840&q=75)
Transcribed Image Text:Show that R2
= span
We must show that for any vector
X
1
(1) (-1)).
1
A+4-8
y
-1
for some x, y. Row-reduce the associated augmented matrix:
1
1
1 -1
a
R₁
+
a
b
So given a and b, we have
b
a
[:]
b
10
- R₂
40
0 1
2
a
>
b
R₂ - R₁
we can write
1 1
0-2
2a - b
2
b-a
2
2a - b
2
X
X
=
1 1
a b
[B]+($- £¸)[4]•B]}]
2 2
-1
b
0 1
b - a
2
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