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Mathematics
Problem
For a system of linear equations represented by
A
X
=
B
AX=B
A
X
=
B
with square matrix
A
A
A
, which of the following conditions guarantees that the system is inconsistent (has no solution)? a)
∣
A
∣
=
0
|A|=0
∣
A
∣
=
0
b)
∣
A
∣
=
0
and
(
a
d
j
A
)
B
≠
0
|A|=0 \text{ and } (\mathrm{adj}A)B\neq 0
∣
A
∣
=
0
and
(
adj
A
)
B
=
0
c)
∣
A
∣
≠
0
|A|\neq 0
∣
A
∣
=
0
d)
∣
A
∣
=
0
and
(
a
d
j
A
)
B
=
0
|A|=0 \text{ and } (\mathrm{adj}A)B=0
∣
A
∣
=
0
and
(
adj
A
)
B
=
0
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