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Suppose A is a 4 x 4 matrix. Let E₁ be the elementary matrix corresponding to switching the first and third rows of A. E1 = Let E2 be the elementary matrix corresponding to multiplying the fourth row of A by 5. Prove: |E₁A| = |E₁| |A|, WITHOUT using the theorem that the determinant of a product is the product of the determinants. Prove: |E2A| = |E2| |A|, WITHOUT using the theorem that the determinant of a product is the product of the determinants.

Suppose A is a 4 x 4 matrix. Let E₁ be the elementary matrix corresponding to switching the first and third rows of A. E1 = Let E2 be the elementary matrix corresponding to multiplying the fourth row of A by 5. Prove: |E₁A| = |E₁| |A|, WITHOUT using the theorem that the determinant of a product is the product of the determinants. Prove: |E2A| = |E2| |A|, WITHOUT using the theorem that the determinant of a product is the product of the determinants.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 34E
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Suppose A is a 4 x 4 matrix. Let E₁ be the elementary matrix corresponding to switching the first and third rows of A. E1 = Let E2 be the elementary matrix corresponding to multiplying the fourth row of A by 5. Prove: |E₁A| = |E₁| |A|, WITHOUT using the theorem that the determinant of a product is the product of the determinants.
Transcribed Image Text:Suppose A is a 4 x 4 matrix. Let E₁ be the elementary matrix corresponding to switching the first and third rows of A. E1 = Let E2 be the elementary matrix corresponding to multiplying the fourth row of A by 5. Prove: |E₁A| = |E₁| |A|, WITHOUT using the theorem that the determinant of a product is the product of the determinants.
Prove: |E2A| = |E2| |A|, WITHOUT using the theorem that the determinant of a product is the product of the determinants.
Transcribed Image Text:Prove: |E2A| = |E2| |A|, WITHOUT using the theorem that the determinant of a product is the product of the determinants.
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