c) Construct an orthogonal matrix P with |P| = 1 that diagonalizes your matrix from a). d) Write the equation of the function in the new coordinate system. e) Identify the type of conic or quadric surface described by the equation. f) Calculate the angle of rotation in degrees. 3. 7x² + 4y² +7z² + 8xz - 15 = 0
c) Construct an orthogonal matrix P with |P| = 1 that diagonalizes your matrix from a). d) Write the equation of the function in the new coordinate system. e) Identify the type of conic or quadric surface described by the equation. f) Calculate the angle of rotation in degrees. 3. 7x² + 4y² +7z² + 8xz - 15 = 0
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
Parts D, E, and F. I attached the photo of the answers to A-C also.
![Part Three
30)
3:3
7x² 4² 72²
7 O
O 4 O
6) A-21=0
0-4
O
7=4
4
7
03
+8x2-15-0
6-₂ O
4-2
4
704
ERES ERSAVEL
CHAR
H
LICHMA
* []
]
(0,1,0]
X-Xy: 0
X₂=0
X₁ X3
V7
[101]
G
(1-7)((4-7)(7-2)) + 4 (-(4-2)-4)
0(7-2)/28-112434)- 16(4-7)
* (7-3)87² +897-132
(2-3)(2²-157 +44)
facher out
1
2= 3
2=4
V1
×2=0
V₁5-x₂
V3:0
P=
PTAP =
12 O 12
ото
E](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24638e23-7712-442e-8ea2-f441f488d4c1%2Ff848a551-0f48-4f78-ba66-18918bdcfb98%2Fx9vsr0a_processed.png&w=3840&q=75)
Transcribed Image Text:Part Three
30)
3:3
7x² 4² 72²
7 O
O 4 O
6) A-21=0
0-4
O
7=4
4
7
03
+8x2-15-0
6-₂ O
4-2
4
704
ERES ERSAVEL
CHAR
H
LICHMA
* []
]
(0,1,0]
X-Xy: 0
X₂=0
X₁ X3
V7
[101]
G
(1-7)((4-7)(7-2)) + 4 (-(4-2)-4)
0(7-2)/28-112434)- 16(4-7)
* (7-3)87² +897-132
(2-3)(2²-157 +44)
facher out
1
2= 3
2=4
V1
×2=0
V₁5-x₂
V3:0
P=
PTAP =
12 O 12
ото
E
Transcribed Image Text:For each quadratic function
a) State the matrix of the quadratic form associated with the given equation.
b) Determine the eigenvalues of the matrix.
c) Construct an orthogonal matrix P with |P| = 1 that diagonalizes your matrix from a).
d) Write the equation of the function in the new coordinate system.
e) Identify the type of conic or quadric surface described by the equation.
f) Calculate the angle of rotation in degrees.
3. 7x² + 4y² +7z² + 8xz − 15 = 0
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