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
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
#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#
