For each of the following quadratic forms, write down the symmetric coefficient matrix A such that Q = VAT and v = [X₁ X₂ ... Xn]. (a) Q (x, y, z) = −x² + 5 xy + 2y² + 2xz+3yz-3 z², (b) Q (x, y) = 2 x² + 4xy + 4y², (c) Q (x, y, z) = −5 x² + 5 x y − 3y² + 5x z + y z + 4 z², A = A = A =
For each of the following quadratic forms, write down the symmetric coefficient matrix A such that Q = VAT and v = [X₁ X₂ ... Xn]. (a) Q (x, y, z) = −x² + 5 xy + 2y² + 2xz+3yz-3 z², (b) Q (x, y) = 2 x² + 4xy + 4y², (c) Q (x, y, z) = −5 x² + 5 x y − 3y² + 5x z + y z + 4 z², A = A = A =
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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![For each of the following quadratic forms, write down the symmetric coefficient matrix A such that Q = vAv¹ and
V = [X₁ X₂
Xn].
(a) Q (x, y, z) = -x² + 5 xy + 2y² + 2xz+3yz-3 z²,
(b) Q (x, y) = 2 x² + 4 xy + 4y²,
(c) Q (x, y, z) = -5x² + 5xy-3y² + 5xz+yz +4z²,
(d) Q (w, x, y, z) = −w² + 2 x² + 2 wy+xy − 5 y² − 5 w z - 4 xz - 5 y z + 3 z²,
(e) Q (x, y) = -2x² + 5xy-4y²,
A =
A
||
A =
A =
=
||
II](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc3c0612-e198-45c8-8e80-98d06c0b64b4%2Fd6001ed9-b787-4d66-a8c8-f3e25e2c1c52%2F3ac6i7_processed.png&w=3840&q=75)
Transcribed Image Text:For each of the following quadratic forms, write down the symmetric coefficient matrix A such that Q = vAv¹ and
V = [X₁ X₂
Xn].
(a) Q (x, y, z) = -x² + 5 xy + 2y² + 2xz+3yz-3 z²,
(b) Q (x, y) = 2 x² + 4 xy + 4y²,
(c) Q (x, y, z) = -5x² + 5xy-3y² + 5xz+yz +4z²,
(d) Q (w, x, y, z) = −w² + 2 x² + 2 wy+xy − 5 y² − 5 w z - 4 xz - 5 y z + 3 z²,
(e) Q (x, y) = -2x² + 5xy-4y²,
A =
A
||
A =
A =
=
||
II
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