Problem 0.6 Given a symmetric matrix A = for A = 69, (3) Diagonalize the matrix QA(x,y) = [x = y] [86] [*] (1) Check by a direct computation that Q₁(x, y) = ax² + 2bxy + cy². (2) Explain what {(x, y) = R² : Q₁(x, y) = 1} represents geometrically, and B = [8] 40 [2], respectively. [31 3 define Can you find an orthogonal matrix V such that VBV-¹ becomes diagonal? (4) Sketch the set {(x, y) = R² : 3x² + 2xy + 3y² = 1}, by relating it with QB, and using the ingredients from (1)-(3).
Problem 0.6 Given a symmetric matrix A = for A = 69, (3) Diagonalize the matrix QA(x,y) = [x = y] [86] [*] (1) Check by a direct computation that Q₁(x, y) = ax² + 2bxy + cy². (2) Explain what {(x, y) = R² : Q₁(x, y) = 1} represents geometrically, and B = [8] 40 [2], respectively. [31 3 define Can you find an orthogonal matrix V such that VBV-¹ becomes diagonal? (4) Sketch the set {(x, y) = R² : 3x² + 2xy + 3y² = 1}, by relating it with QB, and using the ingredients from (1)-(3).
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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![Problem 0.6
Given a symmetric matrix A
for A =
[8],
QA(x, y) = [x_y] [0].
(1) Check by a direct computation that QA(x, y) = ax² + 2bxy + cy².
(2) Explain what {(x, y) = R² : Q₁(x, y) = 1} represents geometrically,
[1], and [2], respectively.
0
(3) Diagonalize the matrix
define
3
B=11
3
Can you find an orthogonal matrix V such that VBV-¹ becomes
diagonal?
(4) Sketch the set
{(x, y) = R² : 3x² + 2xy + 3y² = 1},
by relating it with QB, and using the ingredients from (1)-(3).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ef06bb3-2d9b-4f27-bb3b-835b443ab608%2Fa56b263f-f510-42cd-80a8-a304b0b5c030%2F2xcqzml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 0.6
Given a symmetric matrix A
for A =
[8],
QA(x, y) = [x_y] [0].
(1) Check by a direct computation that QA(x, y) = ax² + 2bxy + cy².
(2) Explain what {(x, y) = R² : Q₁(x, y) = 1} represents geometrically,
[1], and [2], respectively.
0
(3) Diagonalize the matrix
define
3
B=11
3
Can you find an orthogonal matrix V such that VBV-¹ becomes
diagonal?
(4) Sketch the set
{(x, y) = R² : 3x² + 2xy + 3y² = 1},
by relating it with QB, and using the ingredients from (1)-(3).
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