How do you solve using gaussian elimination or gauss-jordan elimination, 2x + 6y = 162x+6y=16, 2x + 3y = -72x+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:
