of k so that the following system has no solutions x1 x2 x

of k so that the following system has no solutions: x_1 - x_2 + x_3 = 1 2x_2 - x_3 = 2 x_2 + kx_3 = 0

Solution

SUbtracting half of second equation from third gives

(k+0.5)x3=-1

So for no solution we must have

k=-0.5

which would make k+0.5=0

For any other value of k we can solve the system as we can solve for x3

So,k=-0.5 for no solutoin