Consider the quadric surface given by -285 x² + 2268 x y-1308 x z+544 y2 - 1344 y z - 1846 z² = 4761 (a) Express this equation in the form x Ax = 4761 where A is a symmetric matrix and x = (O) Enter the matrix A in the box below ab sin (a) a dx 8 α Ω E (b) You are given that the matrix A has eigenvalues 1587, -2116 and -1058. Hence the equation of the surface in terms of its principal axes X, Y and Z can be written as 1587 X2 - 2116 Y2 - 1058 Z² = 4761 Enter the shortest distance, in Maple syntax, from the origin to the surface in the box below.
Consider the quadric surface given by -285 x² + 2268 x y-1308 x z+544 y2 - 1344 y z - 1846 z² = 4761 (a) Express this equation in the form x Ax = 4761 where A is a symmetric matrix and x = (O) Enter the matrix A in the box below ab sin (a) a dx 8 α Ω E (b) You are given that the matrix A has eigenvalues 1587, -2116 and -1058. Hence the equation of the surface in terms of its principal axes X, Y and Z can be written as 1587 X2 - 2116 Y2 - 1058 Z² = 4761 Enter the shortest distance, in Maple syntax, from the origin to the surface in the box below.
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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Transcribed Image Text:This is a three-part question.
Consider the quadric surface given by
(a) Express this equation in the form x Ax = 4761 where A is a symmetric matrix and x =
(0)
Enter the matrix A in the box below
Po
sin (a)
-285 x² + 2268 x y − 1308 x z+ 544 y² – 1344 y z - 1846 z²
ə
əx
f
∞
α
Ω
Note: Use sqrt command when necessary.
E
X
= 4761
(b) You are given that the matrix A has eigenvalues 1587, -2116 and -1058. Hence the equation of the surface in terms of its principal
axes X, Y and Z can be written as
1587 X2 - 2116 Y2 - 1058 Z² = 4761
Enter the shortest distance, in Maple syntax, from the origin to the surface in the box below.
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