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NDA · Maths · Matrices & Determinants
NDA Matrices & Determinants — Formulas 1
Question
1
of 14
1.
For a 3-row determinant with differentiable rows
R
1
,
R
2
,
R
3
R_1, R_2, R_3
R
1
,
R
2
,
R
3
, the derivative
d
d
x
∣
R
1
R
2
R
3
∣
\dfrac{d}{dx}\begin{vmatrix} R_1 \\ R_2 \\ R_3 \end{vmatrix}
d
x
d
R
1
R
2
R
3
equals:
A
∣
R
1
′
R
2
R
3
∣
+
∣
R
1
R
2
′
R
3
∣
\begin{vmatrix}R_1'\\R_2\\R_3\end{vmatrix} + \begin{vmatrix}R_1\\R_2'\\R_3\end{vmatrix}
R
1
′
R
2
R
3
+
R
1
R
2
′
R
3
B
∣
R
1
′
R
2
′
R
3
′
∣
\begin{vmatrix}R_1'\\R_2'\\R_3'\end{vmatrix}
R
1
′
R
2
′
R
3
′
C
∣
R
1
′
R
2
R
3
∣
+
∣
R
1
R
2
′
R
3
∣
−
∣
R
1
R
2
R
3
′
∣
\begin{vmatrix}R_1'\\R_2\\R_3\end{vmatrix} + \begin{vmatrix}R_1\\R_2'\\R_3\end{vmatrix} - \begin{vmatrix}R_1\\R_2\\R_3'\end{vmatrix}
R
1
′
R
2
R
3
+
R
1
R
2
′
R
3
−
R
1
R
2
R
3
′
D
d
d
x
∣
R
1
R
2
R
3
∣
=
∣
R
1
′
R
2
R
3
∣
+
∣
R
1
R
2
′
R
3
∣
+
∣
R
1
R
2
R
3
′
∣
\frac{d}{dx}\begin{vmatrix}R_1\\R_2\\R_3\end{vmatrix} = \begin{vmatrix}R_1'\\R_2\\R_3\end{vmatrix} + \begin{vmatrix}R_1\\R_2'\\R_3\end{vmatrix} + \begin{vmatrix}R_1\\R_2\\R_3'\end{vmatrix}
d
x
d
R
1
R
2
R
3
=
R
1
′
R
2
R
3
+
R
1
R
2
′
R
3
+
R
1
R
2
R
3
′
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