Using cofactors of elements of third column, evaluate \(\Delta = \left| {\begin{array}{*{20}{c}} 1&x&{yz} \\ 1&y&{zx} \\ 1&z&{xy} \end{array}} \right|\)
Find minors and cofactors of the elements of the determinant \(\left| {\begin{array}{*{20}{c}} 2&{ - 3}&5 \\ 6&0&4 \\ 1&5&{ - 7} \end{array}} \right|\) Verify that a11A31 + a12A32 + a13A33 = 0.
Solve the linear programming problem graphically: Maximise Z = 4x + y subject to the constraints: x + y \(\le\) 50 3x + y \(\le\) 90 x \(\ge\) 0, y \(\ge\) 0
Show that the minimum of Z occurs at more than two points. Minimize and Maximize Z = 5x + 10y subject to \(x + 2y \leqslant 120,x + y \geqslant 60\), \(x - 2y \geqslant 0,x,y \geqslant 0\).
Show that the minimum of Z occurs at more than two points. Minimise and maximise \(Z = x + 2y \)subject to \(x + 2 y \geq 100,2 x - y \leq 0,2 x + y \leq 200\)\(x , y \geq 0\)