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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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