3. Suppose A € M5,5 (R) and det(A) = -3. Find each of the following: (a) det(A¹), det (A-¹), det(-2A), det(A²) (b) det(B), where B is obtained from A by performing the following 3 row operations in the given order: (i) 6R₁ + R₂ (ii) 5R3 (iii) R4 R5.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 21EQ: Students frequently perform the following type of calculation to introduce a zero into a matrix:...
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3.
Suppose A € M5,5(R) and det(A) = −3. Find each of the following:
(a) det(A¹), det(A−¹), det(−2A), det(A²)
(b) det(B), where B is obtained from A by performing the following 3 row operations in the
given order:
(i) 6R₁ + R₂
(ii) 5R3
(iii) R4 ↔ R5.
Transcribed Image Text:3. Suppose A € M5,5(R) and det(A) = −3. Find each of the following: (a) det(A¹), det(A−¹), det(−2A), det(A²) (b) det(B), where B is obtained from A by performing the following 3 row operations in the given order: (i) 6R₁ + R₂ (ii) 5R3 (iii) R4 ↔ R5.
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