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(a) State the first three “fundamental properties" of the determinant of a n x n matrix, which completely determine the determinant as a function from n x n matrices to numbers. (b) Explain how it follows from these three properties that the determinant of an n x n matrix with two equal rows is zero.

(a) State the first three “fundamental properties" of the determinant of a n x n matrix, which completely determine the determinant as a function from n x n matrices to numbers. (b) Explain how it follows from these three properties that the determinant of an n x n matrix with two equal rows is zero.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.1: The Determinants Of A Matrix
Problem 70E: The determinant of a 22 matrix involves two products. The determinant of a 33 matrix involves six...
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(a) State the first three "fundamental properties" of the determinant of a n x n matrix, which completely determine the determinant as a function from n x n matrices to numbers. (b) Explain how it follows from these three properties that the determinant of an n x n matrix with two equal rows is zero.
Transcribed Image Text:(a) State the first three "fundamental properties" of the determinant of a n x n matrix, which completely determine the determinant as a function from n x n matrices to numbers. (b) Explain how it follows from these three properties that the determinant of an n x n matrix with two equal rows is zero.
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