2a₁b₁ Let A = ab₂ + a₂b₁ abz+azb a₁b₂+ a₂b₁ 2a₂b₂ azb₂ + a₂b3 a₁b3 + c3b₁ 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) a h b f (I'x + m'y + n), then h g g f = 0. C

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter4: Systems Of Linear Equations
Section4.6: Solve Systems Of Equations Using Determinants
Problem 4.93TI: Evaluate the determinant |324012231| , by expanding by minors along the first row.
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Question
2a₁b₁
Let A = ab₂ + a₂b₁
ab3 +azbi
a₁b₂+d₂b₁
2a₂b₂
azb₂ + a₂b3
a₁b3 +azb
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)
h
b
f
(I'x + m'y + n'), then h
g
g
f = 0.
C
Transcribed Image Text:2a₁b₁ Let A = ab₂ + a₂b₁ ab3 +azbi a₁b₂+d₂b₁ 2a₂b₂ azb₂ + a₂b3 a₁b3 +azb 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) h b f (I'x + m'y + n'), then h g g f = 0. C
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