Linear Algebra Quiz
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Let
A
=
(
a
b
c
d
e
f
g
h
i
)
A = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}
A
=
a
d
g
b
e
h
c
f
i
be a
3
×
3
3 \times 3
3
×
3
matrix with
det
(
A
)
=
4
\det(A) = 4
det
(
A
)
=
4
. Consider the matrix
B
=
(
g
h
i
d
−
2
a
e
−
2
b
f
−
2
c
a
b
c
)
B = \begin{pmatrix} g & h & i \\ d-2a & e-2b & f-2c \\ a & b & c \end{pmatrix}
B
=
g
d
−
2
a
a
h
e
−
2
b
b
i
f
−
2
c
c
. What is the value of
det
(
B
)
\det(B)
det
(
B
)
?
A
−
8
-8
−
8
B
−
4
-4
−
4
C
4
4
4
D
8
8
8
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