Multiple choice

The following simultaneous equations X + y + z = 3 X + 2y + 3z = 4 X + 4y + kz = 6 will NOT have a unique solution for k equal to

  1. 0

  2. 30

  3. 6

  4. 7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A system of equations has no unique solution if the determinant of the coefficient matrix is zero. Matrix: [[1, 1, 1], [1, 2, 3], [1, 4, k]]. Det = 1(2k - 12) - 1(k - 3) + 1(4 - 2) = 2k - 12 - k + 3 + 2 = k - 7. Setting k - 7 = 0 gives k = 7.

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