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Problems
If
Δ
=
∣
a
1
b
1
c
1
a
2
b
2
c
2
a
3
b
3
c
3
∣
\Delta = \begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}
Δ
=
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
…
Mathematics
Problem
If
Δ
=
∣
a
1
b
1
c
1
a
2
b
2
c
2
a
3
b
3
c
3
∣
\Delta = \begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}
Δ
=
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
and
A
1
,
B
1
,
C
1
A_1, B_1, C_1
A
1
,
B
1
,
C
1
denote the cofactors of
a
1
,
b
1
,
c
1
a_1, b_1, c_1
a
1
,
b
1
,
c
1
respectively, then the value of the determinant
∣
A
1
B
1
C
1
A
2
B
2
C
2
A
3
B
3
C
3
∣
\begin{vmatrix} A_1 & B_1 & C_1 \\ A_2 & B_2 & C_2 \\ A_3 & B_3 & C_3 \end{vmatrix}
A
1
A
2
A
3
B
1
B
2
B
3
C
1
C
2
C
3
is (a)
Δ
\Delta
Δ
(b)
Δ
2
\Delta^2
Δ
2
(c)
Δ
3
\Delta^3
Δ
3
(d) 0 (a)
Δ
\Delta
Δ
(b)
Δ
2
\Delta^2
Δ
2
(c)
Δ
3
\Delta^3
Δ
3
(d) 0
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