Consider the quadratic form Q(x, y) = -- 14 28 9 A = 288 -1/ -²+ 14 9 20 56 x y 9 14 9 following principal minors of the matrix A: - The (leading) principal minor 7pm3 = pm3 of order 3: The leading principal minor 1pm² = pm of order 2: The leading principal minor 1pm₁ = pm of order 1: The principal minor pm² of order 2: The principal minor pm² of order 2: The principal minor pm½ of order 1: The principal minor pm of order 1: v2 9 28 x z 9 Now use your answers to classify Q: (No answer given) + 28 y z + We want to classify this using Sylvester's Criteria (the principal minor test). Calculate the 20 Z² 9 with symmetric coefficient matrix
Consider the quadratic form Q(x, y) = -- 14 28 9 A = 288 -1/ -²+ 14 9 20 56 x y 9 14 9 following principal minors of the matrix A: - The (leading) principal minor 7pm3 = pm3 of order 3: The leading principal minor 1pm² = pm of order 2: The leading principal minor 1pm₁ = pm of order 1: The principal minor pm² of order 2: The principal minor pm² of order 2: The principal minor pm½ of order 1: The principal minor pm of order 1: v2 9 28 x z 9 Now use your answers to classify Q: (No answer given) + 28 y z + We want to classify this using Sylvester's Criteria (the principal minor test). Calculate the 20 Z² 9 with symmetric coefficient matrix
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:Consider the quadratic form Q(x, y) = -²
A =
la cla
14
9
ala 10 Ila
28
9
---/-
14
9
14
9
14
9
20
9
56 x y
9
following principal minors of the matrix A:
The (leading) principal minor 1pm3 = pm3 of order 3:
The leading principal minor 1pm² = pm3 of order 2:
The leading principal minor 1pm₁ = pm of order 1:
The principal minor pm² of order 2:
The principal minor pm² of order 2:
The principal minor pm of order 1:
The principal minor pm of order 1:
9
Now use your answers to classify Q: (No answer given)
-28 x z
We want to classify this using Sylvester's Criteria (the principal minor test). Calculate the
28 y z
9
+ 202² with symmetric coefficient matrix
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