Determinants Te...

If two rows of a determinant are identical, then what is the value of the determinant ?

The value of k for which $$kx+3y-k+3=0$$ and $$12x+ky=k$$, have infinite solutions, is?

For positive numbers $$x, y$$ and $$z$$ the numerical value of the determinant $$\begin{vmatrix} 1 & \log_x y & \log_x z \\ \log_y x & 1 & \log_y z \\ \log_z x & \log_z y & 1 \end{vmatrix}$$ is

The number of line segments possible with three collinear points is ________.

If any two adjacent rows or columns of a determinant are interchanged in position, the value of the determinant :

If $$a, b, c$$ are non-zero and different from $$1$$, then the value of $$\begin{vmatrix}\log_a 1 & \log_a b & \log_ac\\ \log_a \left( \dfrac{1}{b} \right ) & \log_b 1 &\log_a \left( \dfrac{1}{c} \right ) \\ \log_a \left( \dfrac{1}{c}\right ) & \log_a c & \log_c 1\end{vmatrix}$$ is

The points (2, -3), (4,3) and (5, k/2) are on the same straight line. The value(s) of k is (are):

 Let a be the  square  matrix  of  order  2 such  that $$A^2 - 4A + 4I  =0$$ where  I is an  identify  matrix  of order  2. .If$$ B = A ^5 - 4A^4 + 6 A^3 +  4A^2 + A $$ then  Det (B)  is equal to

If $$P=\begin{bmatrix} 1 & c & 3\\ 1 & 3 & 3\\ 2 & 4 & 4\end{bmatrix}$$ is the adjoint of a $$3\times 3$$ matrix Q and det.(Q)$$=4$$, then c is equal to.

If $$A$$ is a skew symmetric matrix, then $$\left| A \right| $$ is