Linear Algebra Foundations #8 - Systems of Equations Discussions | Mathematics

2 years ago+ 1 comment

The determinant of the left hand side of the system reduces to D = 2a² - 2a - 4. For the system to have no solution, D = 0, solving the quadratic equation yields:

a² - a - 2 = 0;

(a + 1)(a - 2) = 0;

a = -1, a = 2

The least possible value of a is -1.

2 years ago+ 0 comments

Python3:

if __name__ == "__main__":
  # Compute the 3 x 3 determinant of the system
  # Determinant = 0, when system of equations has *NO SOLUTIONS*
  det = lambda a: a*(2*a - 1) - 1*(a - 2) + 2*(1 - 4)
  
  # Hold all possible alpha values
  lst = list()
  
  # Loop through several values that make det = 0
  for i in range(-100, 101):
    if det(i) == 0:
      lst += [i]
      
  # Return the minimum value
  print(min(lst))

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