[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
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this question on det of matrix for ODE is messing with me. Can you please explain.

 

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[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
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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