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Use Strategy C25 from Unit C4 to find the equation of the quadric x² + 3y² + 5x² − 8xy − 8yz + 3y +3z-6=0 - - 15WRIS in standard form. Which of the six types of non-degenerate quadric is this quadric?

Use Strategy C25 from Unit C4 to find the equation of the quadric x² + 3y² + 5x² − 8xy − 8yz + 3y +3z-6=0 - - 15WRIS in standard form. Which of the six types of non-degenerate quadric is this quadric?

Advanced Engineering Mathematics
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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Use Strategy C25 from Unit C4 to find the equation of the quadric x² + 3y² +5₂² - 8xy − 8yz+3y+3z-6=0 - 15 wens to in standard form. Which of the six types of non-degenerate quadric is this quadric? TORD caibano ens of nottle giv
Transcribed Image Text:Use Strategy C25 from Unit C4 to find the equation of the quadric x² + 3y² +5₂² - 8xy − 8yz+3y+3z-6=0 - 15 wens to in standard form. Which of the six types of non-degenerate quadric is this quadric? TORD caibano ens of nottle giv
Strategy C25 To write the quadric with equation Ax² + By² + C₂² +Fxy + Gyz +Hxz+Jx+ Ky+Lz + M = 0 in standard form, do the following. 1. Introduce matrices: .write down the matrices A = AF H FB G HG C and J = K (C) L 2. Align the axes: • orthogonally diagonalise A to get X₁ 0 0 0 A2 O 0 0 X3 PT AP = ● find (ƒ_g_h) = JTP, and write the quadric in the form λ₁ (x¹)² + λ₂ (y')² + λ3 (2')² + ƒx' + gy' + hz' + M = 0. 3. Translate the origin: • complete the squares • make a substitution to change to the coordinate system (x", y", z").
Transcribed Image Text:Strategy C25 To write the quadric with equation Ax² + By² + C₂² +Fxy + Gyz +Hxz+Jx+ Ky+Lz + M = 0 in standard form, do the following. 1. Introduce matrices: .write down the matrices A = AF H FB G HG C and J = K (C) L 2. Align the axes: • orthogonally diagonalise A to get X₁ 0 0 0 A2 O 0 0 X3 PT AP = ● find (ƒ_g_h) = JTP, and write the quadric in the form λ₁ (x¹)² + λ₂ (y')² + λ3 (2')² + ƒx' + gy' + hz' + M = 0. 3. Translate the origin: • complete the squares • make a substitution to change to the coordinate system (x", y", z").
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