Even if an n × n matrix A fails to be invertible, we can define the adjointadj(A) as in Theorem 6.3.9. The ijthentry of adj(A) is ( − 1 ) 1 + j det ( A j i ) . For which n × n matrices A is ( a d j A ) = 0 ? Give your answer in termsof the rank of A. See Exercise 41.
Even if an n × n matrix A fails to be invertible, we can define the adjointadj(A) as in Theorem 6.3.9. The ijthentry of adj(A) is ( − 1 ) 1 + j det ( A j i ) . For which n × n matrices A is ( a d j A ) = 0 ? Give your answer in termsof the rank of A. See Exercise 41.
Solution Summary: The author explains that the adj(A) matrix is a classical adjoint whose ijth is
Even if an
n
×
n
matrix A fails to be invertible, we can define the adjointadj(A) as in Theorem 6.3.9. The ijthentry of adj(A) is
(
−
1
)
1
+
j
det
(
A
j
i
)
. For which
n
×
n
matrices A is
(
a
d
j
A
)
=
0
? Give your answer in termsof the rank of A. See Exercise 41.
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY