How do you solve using gaussian elimination or gauss-jordan elimination, #2x + 6y = 16#, #2x + 3y = -7#?
1 Answer
(see below for gaus-jordan elimination)
Explanation:
Writing the given equations in augmented matrix form:
#((2,6,16),(2,3,-7))#
Pivot element: row:1, column:1
divide all entries in row 1 by 2 in order to reduce the pivot element to 1
#((1,3,8),(2,3,-7))#
subtract 2 times row 1 from row 2 to zero the non-pivot element in the pivot column
#((1,3,8),(0,-3,-23))#
Pivot element: row:2, column:2
divide all entries in row 2 by (-3) in order to reduce the pivot element to 1
#((1,3,8),(0,1,23/3))#
subtract 3 times row 2 from row 1 to zero the non-pivot element in the pivot column
(this is the step that converts it from gaussian elimination to gaus-jordan elimination)
#((1,0,-15),(0,1,23/3))#
Writing this in non-matrix form:
