Determinants Te...

The point with the co-ordinates $$(2a,\ 3a),\ (3b,\ 2b)$$ & $$(c,\ c)$$ are collinear _____________ .

If lines AB, AC, AD and AE are parallel to a line then_______

The adjoint of the matrix $$\begin{bmatrix} 1 & -2 & 3 \\ 0 & 2 & -1 \\ -4 & 5 & 2 \end{bmatrix}$$ is:

If $$A$$ and $$B$$ are square matrices of same orders then adj. $$(AB)$$ equals

If $$A = (a_{ij})$$ is a $$4\times 4$$ matrix and $$C_{ij}$$ is the co-factor of the element $$a_{ij}$$ in Det (A), then the expression $$a_{11}C_{11} + a_{12}C_{12} + a_{13}C_{13} + a_{14}C_{14}$$ equals

Let $$A = [a_{ij}]_{n\times n}$$ be a square matirx and let $$c_{ij}$$ be cofactor of $$a_{ij}$$ in A. If $$C = [c_{ij}]$$, then

The minors and cofactors of -4 and 9 in determinant $$\begin{vmatrix} -1 & -2 & 3 \\ -4 & -5 & -6 \\ -7 & 8 & 9\end{vmatrix}$$ are respectively

If in the determinant $$\Delta=\begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}, A_i, B_i, C_i$$ etc. be the co-factors of $$a_i, b_i, c_i$$ etc., then which of the following relations is incorrect?

If $$A+B+C=\pi$$, then $$\begin{vmatrix}sin(A+B+C) & sin B & cos C\\ -sinB & 0 & tan A\\ cos(A+B) & -tanA & 0\end{vmatrix}$$ equals

If $$f(x)=\begin{vmatrix} cos x & 1 & 0 \\ 1 & cos x & 1 \\ 0 & 1 & cos x\end{vmatrix}$$ the $$f'(\dfrac \pi 3)$$ equals