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

1 Answer
Bio
Apr 4, 2016

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
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