1. For the matrix A = -1 - 1.1 a. AT b. det A c. A-1 -1 0 2 -1 find the, 2 0 -1
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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Hello, can you please help me with this practice problems?
![1.
2.
3.
For the matrix A=-1
-=&
a. AT
b. det A
c. A-1
1 -1
2
0 -1
Prove that for any two invertible square matrices A and B
(AB)-¹ = B-¹A-¹
(Hint: start from (AB)(AB)−¹ = I )
b. The differential
0
44
-1 find the,
2
(d₁)
[k11 K12 K13]
If d=d₂and K = |k21 k22 K23, where K is symmetric, write
K31 K32 K33¹
(d3)
a. The scalar quadratic form U = dTK d_explicitly
au
əd
|||
au
ad₁
au
in terms of d and K
ad₂
au
მძვ
(Hint: Remember that K is symmetric)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff37479fd-3f26-4b9a-b4ee-9f5a6ec7dc66%2F9c413c8a-c0f9-4179-97d3-8fb1403ef001%2Fpn0u2w9_processed.png&w=3840&q=75)
Transcribed Image Text:1.
2.
3.
For the matrix A=-1
-=&
a. AT
b. det A
c. A-1
1 -1
2
0 -1
Prove that for any two invertible square matrices A and B
(AB)-¹ = B-¹A-¹
(Hint: start from (AB)(AB)−¹ = I )
b. The differential
0
44
-1 find the,
2
(d₁)
[k11 K12 K13]
If d=d₂and K = |k21 k22 K23, where K is symmetric, write
K31 K32 K33¹
(d3)
a. The scalar quadratic form U = dTK d_explicitly
au
əd
|||
au
ad₁
au
in terms of d and K
ad₂
au
მძვ
(Hint: Remember that K is symmetric)
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