The matrix A= set of eigenvectors {v} of A and hence an orthogonal matrix P such that Pt AP is diagonal, or say why this is not possible. Select one: O No such orthogonal matrix P is possible since PT = P-¹ would imply that A is both congruent to and similar to the diagonal matrix by the same P, which is not possible as similarity and congruence are very different concepts. O O 1 1 1 1 2 1 is self-adjoint as a linear map on R³ with its standard inner product. Given that its eigenvalues are 0, 2 ± √2, find an orthonormal 1 1 1 O None of the others apply V1 = V1 = []/ 0 |√3, V₂ = 1 0 √2 |√3, V3 = O One of the eigenvalues is 0 so this matrix A does not define an inner product space. Hence this will not be possible to find such a P 1 C 0 √√√2, v2 = √√2/2, V3 = 1 1/√3 and P = {V₁, V2, V3} 1 -√2/2 and P = {V₁, V2, V3} 1
The matrix A= set of eigenvectors {v} of A and hence an orthogonal matrix P such that Pt AP is diagonal, or say why this is not possible. Select one: O No such orthogonal matrix P is possible since PT = P-¹ would imply that A is both congruent to and similar to the diagonal matrix by the same P, which is not possible as similarity and congruence are very different concepts. O O 1 1 1 1 2 1 is self-adjoint as a linear map on R³ with its standard inner product. Given that its eigenvalues are 0, 2 ± √2, find an orthonormal 1 1 1 O None of the others apply V1 = V1 = []/ 0 |√3, V₂ = 1 0 √2 |√3, V3 = O One of the eigenvalues is 0 so this matrix A does not define an inner product space. Hence this will not be possible to find such a P 1 C 0 √√√2, v2 = √√2/2, V3 = 1 1/√3 and P = {V₁, V2, V3} 1 -√2/2 and P = {V₁, V2, V3} 1
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
![The matrix A=
set of eigenvectors {v} of A and hence an orthogonal matrix P such that Pt AP is diagonal, or say why this is not possible.
Select one:
O
No such orthogonal matrix P is possible since PT = P-¹ would imply that A is both congruent to and similar to the diagonal matrix by the same P, which
is not possible as similarity and congruence are very different concepts.
O
O
1 1 1
1 2 1 is self-adjoint as a linear map on R³ with its standard inner product. Given that its eigenvalues are 0,2 ± √2, find an orthonormal
1 1 1
O
None of the others apply
V1 =
V1 =
[]/
0
|√3, V2 =
1
0
√2
|√3, V3 =
O
One of the eigenvalues is 0 so this matrix A does not define an inner product space. Hence this will not be possible to find such a P
1
C
0 √√√2, v2 = √√2/2, V3 =
1
1/√3 and P = {V₁, V2, V3}
1
-√2/2 and P ={v₁, v2, v3}
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bc9583c-2eed-433e-b3be-99cb5345471a%2F8011a4fd-4d33-44ea-86b3-00ddddd5ab61%2F12xshs_processed.png&w=3840&q=75)
Transcribed Image Text:The matrix A=
set of eigenvectors {v} of A and hence an orthogonal matrix P such that Pt AP is diagonal, or say why this is not possible.
Select one:
O
No such orthogonal matrix P is possible since PT = P-¹ would imply that A is both congruent to and similar to the diagonal matrix by the same P, which
is not possible as similarity and congruence are very different concepts.
O
O
1 1 1
1 2 1 is self-adjoint as a linear map on R³ with its standard inner product. Given that its eigenvalues are 0,2 ± √2, find an orthonormal
1 1 1
O
None of the others apply
V1 =
V1 =
[]/
0
|√3, V2 =
1
0
√2
|√3, V3 =
O
One of the eigenvalues is 0 so this matrix A does not define an inner product space. Hence this will not be possible to find such a P
1
C
0 √√√2, v2 = √√2/2, V3 =
1
1/√3 and P = {V₁, V2, V3}
1
-√2/2 and P ={v₁, v2, v3}
1
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