exam Maths Puzzle Numerical Ability

how we can do minimization of multiple variable function with constraint

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exam Other Question

find the value of k so that the system of the equation
x+y+3z=0
4x+3y+kz=0
2x+y+2z=0 has no a non trival solution Find the inverse (A^-1) if the following matrix.

A=[3 1]
[-1 2]