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1. A quadratic surface has equation 3a²-x²-x³+4x²₁x₂ + 4x₁23 +12x2x3 = 1. (a) Write this equation in the form x¹ Ax = 1. (b) Find eigenvalues of the matrix A and the corresponding unit eigenvec- tors.

1. A quadratic surface has equation 3a²-x²-x³+4x²₁x₂ + 4x₁23 +12x2x3 = 1. (a) Write this equation in the form x¹ Ax = 1. (b) Find eigenvalues of the matrix A and the corresponding unit eigenvec- tors.

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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Please solve the quadratic surface question. If possible please answer all with solutions thank you

1. A quadratic surface has equation 3x²-x²-x² + 4x1x2 + 4x1x3 + 12x2x3 = 1. (a) Write this equation in the form x² Ax = 1. (b) Find eigenvalues of the matrix A and the corresponding unit eigenvec- tors. (c) Write down the spectral matrix, the new (canonical) variables y₁, Y2 and y3 in terms of the original variables 1, 2 and 23, and the canonical form of the equation to the surface in terms of the new variables. (d) Identify the surface.
Transcribed Image Text:1. A quadratic surface has equation 3x²-x²-x² + 4x1x2 + 4x1x3 + 12x2x3 = 1. (a) Write this equation in the form x² Ax = 1. (b) Find eigenvalues of the matrix A and the corresponding unit eigenvec- tors. (c) Write down the spectral matrix, the new (canonical) variables y₁, Y2 and y3 in terms of the original variables 1, 2 and 23, and the canonical form of the equation to the surface in terms of the new variables. (d) Identify the surface.
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