Determinants Te...

If $$a, b$$ and $$c$$ are in $$AP$$, then determinant $$\begin{vmatrix}x + 2 & x + 3 & x + 2a\\ x + 3 & x + 4 & x + 2b\\ x + 4 & x + 5 & x + 2c\end{vmatrix}$$ is

If $$\triangle (r) = \begin{vmatrix}r & r^{3}\\ 1 & n(n + 1)\end{vmatrix}$$, then $$\displaystyle \sum_{r = 1}^{n} \triangle (r)$$ is equal to

If the points $$(2,5),(4,6)$$ and $$(a,a)$$ are collinear, then the value of $$a$$ is equal to

If A is an invertible matrix, then what is $$det$$ $$(A^{-1})$$ equal to?

If $$ A = \begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix} $$ and $$ B = \begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$$ then what is determinant of AB ?

If $$\begin{vmatrix} 8 & -5 & 1 \\ 5 & x & 3\\ 6 & 3 & 1 \end{vmatrix} = 2 $$ then what is the value of $$x$$ ?

The cofactor of the element $$4$$ in the determinant
                    $$\begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 5 & 8 & 9 \end{vmatrix}$$
is

If $$\begin{vmatrix} 6i & -3i & 1 \\ 4 & 3i & -1\\ 20 & 3 & i\end{vmatrix} =x+iy,$$ where $$i=\sqrt{-1}$$, then what is x equal to?

If $$\begin{vmatrix} a & b & 0 \\ 0 & a & b \\ b & 0 & a\end{vmatrix}=0$$, then which one of the following is correct?

Which of the following are correct in respect of the system of equations $$x + y + z = 8, x - y + 2z = 6$$ and $$3x - y + 5z = k$$?
1. They have no solution, if $$k = 15$$.
2. They have infinitely many solutions, if $$k = 20$$.
3. They have unique solution, if $$k = 25$$.
Select the correct answer using the code given below