Let a, b, c and d be constants and define 1 a a² a³ 1 b b? b³ A = 1 1 d d d3 Without using cofactor expansion, prove that det(A) = (d – a)(c – a)(b – a)(d – b)(c – b)(d – c). %3D

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let a, b, c and d be constants and define
1
a a? q3
1 b b² b³
A =
1
c ? 3
1 d d d3
Without using cofactor expansion, prove that
det (A) %3D (d — а)(с - а)(6 — а)(d — b)(с- b)(а — с).
Transcribed Image Text:Let a, b, c and d be constants and define 1 a a? q3 1 b b² b³ A = 1 c ? 3 1 d d d3 Without using cofactor expansion, prove that det (A) %3D (d — а)(с - а)(6 — а)(d — b)(с- b)(а — с).
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