Det A= -3 and B= 2 determine the following a) det (AB) b) det (3B) c) det [(AB)^T] d) det (B^-1) e) det (B^3)
Det A= -3 and B= 2 determine the following a) det (AB) b) det (3B) c) det [(AB)^T] d) det (B^-1) e) det (B^3)
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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Question
Det A= -3 and B= 2 determine the following a) det (AB)
b) det (3B)
c) det [(AB)^T]
d) det (B^-1)
e) det (B^3)
Expert Solution
Step 1
We assume A and B are matrices of order n.
Now, Det(A) = -3
Det(B) = 2.
(a) Det(AB) = Det(A).Det(B) = (-3)×2 = -6
(b) Det(3B) = 3nDet(B) = 3n.2 = 2.3n
(c) Det{(AB)T} = Det(AB) = -6
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