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.
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6f76b1b-4dc8-4fb6-ba6c-71c6e499db43%2F581a0458-0367-4ed5-931f-9340e2df2dae%2Fd75koq7_processed.png&w=3840&q=75)
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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