D = 12 x y Consider the quadratic form Q(x, y) = 8² + Find a diagonal matrix D and an orthogonal matrix P such that A = P¹ DP. P = + 17 ² 5 Use the orthogonal transformation V = Pv, where v = Q(X,Y) = aX² + bY² for some a and b. X = Y = Q(X,Y) = with symmetric coefficient matrix A = [*] and V = [X] colin 6in 655 to find variables X and Y such that By inspection of Q(X, Y) (or, equivalently, using the eigenvalue test) what is the sign property of the quadratic form Q? (No answer given) ◆
D = 12 x y Consider the quadratic form Q(x, y) = 8² + Find a diagonal matrix D and an orthogonal matrix P such that A = P¹ DP. P = + 17 ² 5 Use the orthogonal transformation V = Pv, where v = Q(X,Y) = aX² + bY² for some a and b. X = Y = Q(X,Y) = with symmetric coefficient matrix A = [*] and V = [X] colin 6in 655 to find variables X and Y such that By inspection of Q(X, Y) (or, equivalently, using the eigenvalue test) what is the sign property of the quadratic form Q? (No answer given) ◆
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
![12 x y
+
5
Find a diagonal matrix D and an orthogonal matrix P such that A = PT DP.
Consider the quadratic form Q(x, y) =
D =
P: =
8x²
5
+
Use the orthogonal transformation V = Pv, where v =
Q(X,Y) = aX² + by2 for some a and b.
X =
Y =
Q(X,Y)=
17 y²
5
[x]
V
with symmetric coefficient matrix A =
and V =
X
M.
जानकाळ
65
17
5
to find variables X and Y such that
By inspection of Q(X, Y) (or, equivalently, using the eigenvalue test) what is the sign property of the quadratic form Q?
(No answer given) ♦](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc3c0612-e198-45c8-8e80-98d06c0b64b4%2Fe4fcd62f-bf14-4f88-b38a-d7f3df9b8741%2F7orgses_processed.png&w=3840&q=75)
Transcribed Image Text:12 x y
+
5
Find a diagonal matrix D and an orthogonal matrix P such that A = PT DP.
Consider the quadratic form Q(x, y) =
D =
P: =
8x²
5
+
Use the orthogonal transformation V = Pv, where v =
Q(X,Y) = aX² + by2 for some a and b.
X =
Y =
Q(X,Y)=
17 y²
5
[x]
V
with symmetric coefficient matrix A =
and V =
X
M.
जानकाळ
65
17
5
to find variables X and Y such that
By inspection of Q(X, Y) (or, equivalently, using the eigenvalue test) what is the sign property of the quadratic form Q?
(No answer given) ♦
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Step 1: Write the given data
VIEWStep 2: Finding the eigenvalues of the coefficient matrix
VIEWStep 3: Determine the corresponding orthonormal eigenvectors
VIEWStep 4: Determine the corresponding orthonormal eigenvectors
VIEWStep 5: Consider an orthogonal matrix P and a diagonal matrix D
VIEWStep 6: Convert the given quadratic into its diagonal form using the given orthogonal transformation
VIEWStep 7: Determine the sign property
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