Let A = ( a i j ) be the ( n × n ) matrix specified thus: a i j = d for i = j and a i j = 1 for i ≠ j . For n = 2 , 3 , and 4, show that det ( A ) = ( d − 1 ) n − 1 ( d − 1 + n ) .
Let A = ( a i j ) be the ( n × n ) matrix specified thus: a i j = d for i = j and a i j = 1 for i ≠ j . For n = 2 , 3 , and 4, show that det ( A ) = ( d − 1 ) n − 1 ( d − 1 + n ) .
Solution Summary: The author explains that the determinant of the matrix will be given according to the equation mathrmdet(A)=(d-1)n-1 (d-1+n)
Let
A
=
(
a
i
j
)
be the
(
n
×
n
)
matrix specified thus:
a
i
j
=
d
for
i
=
j
and
a
i
j
=
1
for
i
≠
j
. For
n
=
2
,
3
,
and 4,
show that
det
(
A
)
=
(
d
−
1
)
n
−
1
(
d
−
1
+
n
)
.
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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