Let A = [ a i j ( t ) ] be an m × n matrix function and let B = [ b i j ( t ) ] be an n × p matrix function. Use the definition of matrix multiplication to prove that d d t ( A B ) = A d B d t + d A d t B .
Let A = [ a i j ( t ) ] be an m × n matrix function and let B = [ b i j ( t ) ] be an n × p matrix function. Use the definition of matrix multiplication to prove that d d t ( A B ) = A d B d t + d A d t B .
Solution Summary: The author explains how the derivative of matrix function is obtained by differentiating every element of the matrix.
Let
A
=
[
a
i
j
(
t
)
]
be an
m
×
n
matrix function and let
B
=
[
b
i
j
(
t
)
]
be an
n
×
p
matrix function. Use the definition of matrix multiplication to prove that
d
d
t
(
A
B
)
=
A
d
B
d
t
+
d
A
d
t
B
.
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HOW TO FIND DETERMINANT OF 2X2 & 3X3 MATRICES?/MATRICES AND DETERMINANTS CLASS XII 12 CBSE; Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=bnaKGsLYJvQ;License: Standard YouTube License, CC-BY