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Mathematics
Mathematics
Problem
Let
A
=
(
1
2
k
0
3
−
1
4
−
2
5
)
,
A = \begin{pmatrix} 1 & 2 & k\\ 0 & 3 & -1\\ 4 & -2 & 5 \end{pmatrix},
A
=
1
0
4
2
3
−
2
k
−
1
5
,
where
k
k
k
is a real number. (a) Obtain
adj
A
\operatorname{adj}A
adj
A
in terms of
k
k
k
. (b) If the
(
2
,
3
)
(2,3)
(
2
,
3
)
-entry of
adj
A
\operatorname{adj}A
adj
A
equals
7
7
7
, determine the value of
k
k
k
.
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