[a11(t) a12(t) 1) Let A(T) = be differentiable. %3D Show that: d (det (A(t)) = det a 12 (t)] la21(t) a22(t) a11(t) a12(t) + det la'21 (t) a'22(t). dt
[a11(t) a12(t) 1) Let A(T) = be differentiable. %3D Show that: d (det (A(t)) = det a 12 (t)] la21(t) a22(t) a11(t) a12(t) + det la'21 (t) a'22(t). dt
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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this question on det of matrix for ODE is messing with me. Can you please explain.
Thanks
![[a11(t) a12(t)
1) Let A(T) = \a21 (t) az2(t)
be differentiable.
Show that:
d
(det (A(t)) = det
a 11(t) a
a21(t) a22(t)
+ det a11(t)
La'21 (t) a'22(t).
a12 (t)
dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0548f28d-2867-4ce8-91e2-809a65372be3%2F0742e507-5165-4021-b602-658475d0f6ac%2Fnj4e99m_processed.png&w=3840&q=75)
Transcribed Image Text:[a11(t) a12(t)
1) Let A(T) = \a21 (t) az2(t)
be differentiable.
Show that:
d
(det (A(t)) = det
a 11(t) a
a21(t) a22(t)
+ det a11(t)
La'21 (t) a'22(t).
a12 (t)
dt
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