How do you solve using gaussian elimination or gauss-jordan elimination, #3x+2y = -9#, #-10x + 5y = - 5#?

1 Answer
Mar 16, 2017

Answer:

See below

Explanation:

First create the augmented matrix:

#((3,2),(-10,5))((-9),(-5))#

For Gaussian elimination , we eliminate by combining rows to get a lower triangle matrix.

#R2 to R2 + 10/3 R1#
#((3,2),(0,35/3))((-9),(-35))#

Then back substitute, so from the second row:

#35/3 y = - 35 implies y -3#

From first row:

#3x + 2y = - 9 implies x = (-9 - 2(-3))/(3) = -1#

For Gauss-Jordan elimination , we row reduce to the identity matrix ie #A mathbf x = mathbf b to I mathbf x = mathbf b'#. So the first step can be the same:

#R2 to R2 + 10/3 R1#
#((3,2),(0,35/3))((-9),(-35))#

Then we can do this:
#R1 to R1 - R2 cdot 6/35#
#((3,0),(0,35/3))((-3),(-35))#

Finally we divide each row by its pivot, ie:

#((3/3,0),(0,(35/3)/(35/3)))((-3/3),(-35/(35/3)))#

#implies ((1,0),(0,1))((-1),(-3))#