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Mathematics
Problem
Let
Δ
1
=
det
(
x
1
y
1
1
x
2
y
2
1
x
3
y
3
1
)
\Delta_1=\det\begin{pmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{pmatrix}
Δ
1
=
det
x
1
x
2
x
3
y
1
y
2
y
3
1
1
1
and
Δ
2
=
det
(
x
1
y
1
1
x
3
y
3
1
x
2
y
2
1
)
\Delta_2=\det\begin{pmatrix}x_1&y_1&1\\x_3&y_3&1\\x_2&y_2&1\end{pmatrix}
Δ
2
=
det
x
1
x
3
x
2
y
1
y
3
y
2
1
1
1
. Which relation between
Δ
1
\Delta_1
Δ
1
and
Δ
2
\Delta_2
Δ
2
is always true? a)
Δ
2
=
0
\Delta_2=0
Δ
2
=
0
b)
Δ
2
=
−
Δ
1
\Delta_2=-\Delta_1
Δ
2
=
−
Δ
1
c)
Δ
2
=
Δ
1
\Delta_2=\Delta_1
Δ
2
=
Δ
1
d)
Δ
2
=
2
Δ
1
\Delta_2=2\Delta_1
Δ
2
=
2
Δ
1
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