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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 22RE
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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
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
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
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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