How do you solve the following linear system #5x - 4y + 4z = 18, -x + 3y - 2z = 0, 4x - 2y + 7z = 3 #?

1 Answer
Apr 4, 2016

Answer:

Either solve using matrices or use elimination

Explanation:

The following system of linear equations, when written in matrix form, is

#((5,-4,4),(-1,3,-2),(4,-2,7)) ((x),(y),(z)) = ((18),(0),(3))#

Assuming you know how to find the determinant of a #3 xx 3# matrix, we can apply Cramer's Rule.

#x = frac{det((18,-4,4),(0,3,-2),(3,-2,7))}{det((5,-4,4),(-1,3,-2),(4,-2,7))}#

#= frac{294}{49}#

#= 6#

#y = frac{det((5,18,4),(-1,0,-2),(4,3,7))}{det((5,-4,4),(-1,3,-2),(4,-2,7))}#

#= frac{0}{49}#

#= 0#

#z = frac{det((5,-4,18),(-1,3,0),(4,-2,3))}{det((5,-4,4),(-1,3,-2),(4,-2,7))}#

#= frac{-147}{49}#

#= -3#

Therefore,

  • #x = 6#
  • #y = 0#
  • #z = -3#