# Math - system of eqns

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Consider the system of equations:

x1 + x2 + x3 = 6,
−x1 − 2x2 + 3x3 = 1,
3x1 − 4x2 + 4x3 = 5.

(a) Write down the augmented matrix for this system

(b) Use elementary row operations to reduced the augmented matrix to reduced row-ecehelon form

FOR A: Ive got:

1 1 1 | 6
-1 -2 3 | 1
3 -4 4 | 5

I need help with B thanks.

• Math - system of eqns -

1 0 0 41 /27

0 1 0 59/27

0 0 1 62 /27

• Math - system of eqns -

How did you get that though

• Math - system of eqns -

1 1 1 | 6
-1 -2 3 | 1
3 -4 4 | 5

1 1 1 | 6
0 -1 4 | 7 from: add #1 and #2
0 7 -1 | 13 from #3 x 1 - #3

1 1 1 | 6
0 -1 4 | 7
0 0 27| 62 from #2 x 7 + #3

1 1 1 6
0 1 -4 -7 switch signs
0 0 1 62/27 divide by 27

so x3 = 62/27
now back substitute
x2 - 4(62/27) = -7
x2 = 248/27 -7 = 59/27
x1 + 59/27 + 62/27 = 6
x1 = 41/27

x1=41/27 , x2=59/27, x3=62/27

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