Question

How would you solve this matrices using the Gauss-jordan elimination method?

{[-5, 8, 10]}
{[5, 8, 4]}
{[10, 8, 5]}
{[5, 4, 8]}

Answer 1

-5 +5 10 +5
+8 +8 +8 +4
10 +4 +5 +8
divide row 1 by -5
+1 -1 -2 -1
+8 +8 +8 +4 subtract 8 -8 -16 -8
10 +4 +5 +8 subtract 10 =10 -20 -10
gives
+1 -1 -2 -1
+0 16 24 12
+0 14 25 18
divide row 2 by 16
+1 -1 -2 -1
+0 +1 1.5 .75 add to row 1-> new row 1
+0 14 25 18
gives
+1 0 -.5 -.25
+0 +1 1.5 .75 times 14 =0 14 21 21/2
+0 14 25 18
subtract row 2 times 14 from row 3
+1 0 -.5 -.25
+0 +1 1.5 .75
+0 +0 -4 -7.5 over 8 add to row 1
gives
+1 0 +0 +5.5/8
+0 +1 1.5 .75
+0 +0 -4 -7.5 divide by -4
then
+1 +0 +0 5.5/8
+0 +1 1.5 .75
+0 +0 +1 7.5/4 times 1.5, subtract from 2
then
+1 +0 +0 5.5/8
+0 +1 +0 -16.5/8
+0 +0 +1 7.5/4
so
x = 55/80 = .6875
y = -165/80 = -2.0625
z = 150/80 = 1.875

Answer 2

I did not bother to check all that, check my answers back in.