A as the product of two determinants, show that A = 0. Hence, show that if ax² + 2hxy + by² + 2gx + 2fy + c = (x + my + n)

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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Question
2a₁b₁
Let A = ab₂ + a₂b₁
ab₂ + a₂b
a₁b₂+ a₂b₁
2a₂b₂
azb₂ + a₂bz
a₁b3 + a₂b₁
a₂b3 + a3b₂. Expressing
2a3b3
A as the product of two determinants, show that A = 0. Hence,
show that if ax² + 2hxy + by2 + 2gx + 2fy + c = (x + my + n)
la
h
(l'x + m'y + n'), then h
b
g
f
g
f = 0.
с
Transcribed Image Text:2a₁b₁ Let A = ab₂ + a₂b₁ ab₂ + a₂b a₁b₂+ a₂b₁ 2a₂b₂ azb₂ + a₂bz a₁b3 + a₂b₁ a₂b3 + a3b₂. Expressing 2a3b3 A as the product of two determinants, show that A = 0. Hence, show that if ax² + 2hxy + by2 + 2gx + 2fy + c = (x + my + n) la h (l'x + m'y + n'), then h b g f g f = 0. с
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