True or false. Please explain your answer. Let A and B be two nxn matrices. a) b) c) d) If B is a matrix obtained from A by adding k times row i to row j then det(B) = k. det (A). A = [a₁ a2 det(A) = det([a₁ + b a₂ ... an] and b be a linear combination of a₁, A2,..., an, then an]). det(AB) - det(BA) = 0. det(AB - BA) = 0. Every orthogonal matrix has determinant = 1.
True or false. Please explain your answer. Let A and B be two nxn matrices. a) b) c) d) If B is a matrix obtained from A by adding k times row i to row j then det(B) = k. det (A). A = [a₁ a2 det(A) = det([a₁ + b a₂ ... an] and b be a linear combination of a₁, A2,..., an, then an]). det(AB) - det(BA) = 0. det(AB - BA) = 0. Every orthogonal matrix has determinant = 1.
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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![True or false. Please explain your answer.
Let A and B be two nx n matrices.
(a)
(b)
(c)
(d)
(e)
If B is a matrix obtained from A by adding k times row i to row j then det(B) =
k · det (A).
A = [a₁ A2
det(A) = det([a₁ + b a₂
an] and b be a linear combination of a₁, A2, ..., an, then
an]).
det(AB) – det(BA) = 0.
det(AB – BA) = 0.
Every orthogonal matrix has determinant 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3eabad6-73f9-4802-abcb-1ea3933fc3f2%2F3e36e269-dc99-4881-bb98-9cfe34c632a8%2Fp3tkizol_processed.png&w=3840&q=75)
Transcribed Image Text:True or false. Please explain your answer.
Let A and B be two nx n matrices.
(a)
(b)
(c)
(d)
(e)
If B is a matrix obtained from A by adding k times row i to row j then det(B) =
k · det (A).
A = [a₁ A2
det(A) = det([a₁ + b a₂
an] and b be a linear combination of a₁, A2, ..., an, then
an]).
det(AB) – det(BA) = 0.
det(AB – BA) = 0.
Every orthogonal matrix has determinant 1.
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