7. Let f(x) = A. Compute Vƒ (x). Show that Vf(x) = 0 if and only if æ is an eigenvector of A.
7. Let f(x) = A. Compute Vƒ (x). Show that Vf(x) = 0 if and only if æ is an eigenvector of A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please send handwritten solution for Q 7
![1. Let A = |0 0. What is the range space of A? What is the rank of A?
|0 2
What is the null space of A and the null space of AT.
[1 2]
2. Obtain the eigendecomposition of A =
2 1
Use the eigendecomposi-
tion to obtain Tr A and det A. Find ||A||2 and ||A|| F.
3. Let a = |ị x2 13
T4 05]*. Find det(I+ aa"). Find ||a||?.
4. Let X € R"xm Show that XxTx>0.
5. Let y = f(x) = t, where A E Rmxm is non-singular, 6, x, C e R",
d e R. Find the inverse_function, i.e., find f-1 such that x = f-'(y).
is non-singular.
[A b]
Assume that Q =
6. Show that for A symmetric inf, A
: Amin (A).
7. Let f(x) = LA. Compute Vf(x). Show that Vf(x) = 0 if and only if x
is an eigenvector of A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75ae2e4d-45e8-40ab-b125-fd4a765c379c%2Fb65115ef-be54-44aa-9f3a-f278c38e347f%2Frs705w_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let A = |0 0. What is the range space of A? What is the rank of A?
|0 2
What is the null space of A and the null space of AT.
[1 2]
2. Obtain the eigendecomposition of A =
2 1
Use the eigendecomposi-
tion to obtain Tr A and det A. Find ||A||2 and ||A|| F.
3. Let a = |ị x2 13
T4 05]*. Find det(I+ aa"). Find ||a||?.
4. Let X € R"xm Show that XxTx>0.
5. Let y = f(x) = t, where A E Rmxm is non-singular, 6, x, C e R",
d e R. Find the inverse_function, i.e., find f-1 such that x = f-'(y).
is non-singular.
[A b]
Assume that Q =
6. Show that for A symmetric inf, A
: Amin (A).
7. Let f(x) = LA. Compute Vf(x). Show that Vf(x) = 0 if and only if x
is an eigenvector of A.
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