Let matrix $$X = [{x_{ij}}]$$ is given by $$X = \left[ {\matrix{ 1 & { - 1} & 2 \cr 3 & 4 & { - 5} \cr 2 & { - 1} & 3 \cr } } \right]$$. Then the matrix $$Y = [{m_{ij}}]$$, where m_ij = Minor of x_ij, is

A function f : R $$\to$$ R defined by f(x) = 2 + x² is

A Linear Programming Problem is as follows:

Maximize/Minimize objective function Z = 2x $$-$$ y + 5

Subject to the constraints

3x + 4y $$\le$$ 60

x + 3y $$\le$$ 30

x $$\ge$$ 0, y $$\ge$$ 0

If the corner points of the feasible region are A (0, 10), B (12, 6), C (20, 0) and O (0, 0) then which of the following is true?

If x = $$-$$4 is a root of $$\left| {\matrix{ x & 2 & 3 \cr 1 & x & 1 \cr 3 & 2 & x \cr } } \right| = 0$$, then the sum of the other two roots is