Question

Solve the system of linear equations represented by this augmented matrix?
[2 -2 1|3]
[3 1 -1|7]
[1 -3 2|0]

(a) (2,0, -1)
(b) (2, -1, 0)
(c) (0, 2, -1)
(d) (-1, 0, 2)

Answer 1

you should prolly just work the elementary row operations for it

Answer 2

what

Answer 3

elementary row operations; its how you work out a matrix:

1) rows and be swapped
2) rows can be added together
3) rows can be multiplied by a scalar

id start by scaling by the LCM of the first column

[2 -2 1|3] * 3
[3 1 -1|7] * -2
[1 -3 2|0] * -6


[ 6 -6 3 9 ]
[-6 -2 2 -14]
[-6 18 -12 0 ]

the add stuff

[ 6 -6 3 9 ]
[ 0 -8 5 -5 ]
[ 0 12 -9 9 ]

etc ....

Answer 4

you eventually reduce the matrix to an identity on the left, and the solution on right

Answer 5

i'm confused

Answer 6

...

[ 1 0 0 x ]
[ 0 1 0 y ]
[ 0 0 1 z ]


then you really should review the ways that you can manipulate the elements of a matrix by row operations

Answer 7

it looks to me like we can then scale row 1 and row 3 by 1/3, and row 2 by -1

[ 6 -6 3 9 ] /3
[ 0 -8 5 -5 ] *-1
[ 0 12 -9 9 ] /3

[ 2 -2 1 3 ]
[ 0 8 -5 5 ]
[ 0 4 -3 3 ]

then its a matter of the LCM of column 2, which looks to be 8

[ 2 -2 1 3 ] *4
[ 0 8 -5 5 ]
[ 0 4 -3 3 ] *-2


[ 8 -8 4 12 ]
[ 0 8 -5 5 ]
[ 0 -8 6 -6 ]

and add again

[ 8 0 -1 17 ]
[ 0 8 -5 5 ]
[ 0 0 1 -1 ]

Answer 8

the process is time consuming, and if you make a mistake early on it just carried thru and makes a mess of things ....im pretty sure i made an error along the way