+13 For a certain value of k, the system
x + y + 3z &= 10,
-4x + 2y + 5z &= 7,
kx + z &= 3
has no solutions. What is this value of k?
+624 The system
x + y + 3z = 10,
-4x + 2y + 5z = 7,
kx + z = 3
will have no solution if the corresponding matrix
[1 1 3]
[-4 2 5]
[k 0 1]
has a determinant of 0. Taking determinant, we find that it is 2k - 14.
Therefore, the value of k such that the system has no solution is k = 7.
