2. Let A be any 4 × 4 matrix with determinant -2. (a) Let N be the matrix obtained from A by applying the row operation -4R₁ R₁. Show how to find det N without knowing the terms of A. (b) Let P be the matrix obtained from A by applying the row operation R₁ ↔ R3. Show how to find det P without knowing the terms of A. (c) Let B be the matrix obtained from A by applying the row operation R₁ - 2R2 → R₁. Show how to find det B without knowing the terms of A.

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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2. Let A be any 4 × 4 matrix with determinant -2.
(a) Let N be the matrix obtained from A by applying the row operation -4R₁ R₁. Show how to
find det N without knowing the terms of A.
(b) Let P be the matrix obtained from A by applying the row operation R₁ ↔ R3. Show how to find
det P without knowing the terms of A.
(c) Let B be the matrix obtained from A by applying the row operation R₁ - 2R2 → R₁. Show how
to find det B without knowing the terms of A.
Transcribed Image Text:2. Let A be any 4 × 4 matrix with determinant -2. (a) Let N be the matrix obtained from A by applying the row operation -4R₁ R₁. Show how to find det N without knowing the terms of A. (b) Let P be the matrix obtained from A by applying the row operation R₁ ↔ R3. Show how to find det P without knowing the terms of A. (c) Let B be the matrix obtained from A by applying the row operation R₁ - 2R2 → R₁. Show how to find det B without knowing the terms of A.
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