How do you solve using gaussian elimination or gauss-jordan elimination, $y + z = - 3$ $y+z=-3$ , $x - y + z = - 7$ $x-y+z=-7$ , $x + y = 2$ $x+y=2$ ?

Question

How do you solve using gaussian elimination or gauss-jordan elimination, $y + z = - 3$ $y+z=-3$ , $x - y + z = - 7$ $x-y+z=-7$ , $x + y = 2$ $x+y=2$ ?

1 Answer

Impact of this question

1488 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-28T08:13:35

$x = 0, y = 2 and z = - 5$ $x =0, y =2 and z =-5$

Explanation:

$r_{1} \to$ $r_1 ->$ $0$ $0$ ........ $1$ $1$ ........ $1$ $1$ ........ $- 3$ $-3$
$r_{2} \to$ $r_2 ->$ $1$ $1$ .... $- 1$ $-1$ ........ $1$ $1$ ........ $- 7$ $-7$
$r_{3} \to$ $r_3 ->$ $1$ $1$ ........ $1$ $1$ ........ $0$ $0$ ............ $2$ $2$

$r_{1} = r_{1} + r_{2}$ $r_1 = r_1 + r_2$
$1$ $1$ ........ $0$ $0$ ........ $2$ $2$ ........ $- 10$ $-10$
$1$ $1$ .... $- 1$ $-1$ ........ $1$ $1$ ........ $- 7$ $-7$
$1$ $1$ ........ $1$ $1$ ........ $0$ $0$ ............ $2$ $2$

$r_{2} = r_{1} - r_{2}$ $r_2 = r_1 - r_2$
$1$ $1$ ........ $0$ $0$ ........ $2$ $2$ ........ $- 10$ $-10$
$0$ $0$ ........ $1$ $1$ ........ $1$ $1$ ........ $- 3$ $-3$
$1$ $1$ ........ $1$ $1$ ........ $0$ $0$ ............ $2$ $2$

$r_{3} = r_{3} - r_{1}$ $r_3 = r_3 - r_1$
$1$ $1$ ........ $0$ $0$ ........ $2$ $2$ ........ $- 10$ $-10$
$0$ $0$ ........ $1$ $1$ ........ $1$ $1$ ........ $- 3$ $-3$
$0$ $0$ ........ $1$ $1$ .... $- 2$ $-2$ ........... $12$ $12$

$r_{3} = r_{3} - r_{2}$ $r_3 = r_3 - r_2$
$1$ $1$ ........ $0$ $0$ ........ $2$ $2$ ........ $- 10$ $-10$
$0$ $0$ ........ $1$ $1$ ........ $1$ $1$ ........ $- 3$ $-3$
$0$ $0$ ........ $0$ $0$ .... $- 3$ $-3$ ........... $15$ $15$

$r_{3} = \frac{r_{3}}{- 3}$ $r_3 = r_3/-3$
$1$ $1$ ........ $0$ $0$ ........ $2$ $2$ ........ $- 10$ $-10$
$0$ $0$ ........ $1$ $1$ ........ $1$ $1$ ........ $- 3$ $-3$
$0$ $0$ ........ $0$ $0$ ........ $1$ $1$ ........ $- 5$ $-5$

$r_{2} = r_{2} - r_{3}$ $r_2 = r_2 - r_3$
$1$ $1$ ........ $0$ $0$ ........ $2$ $2$ ........ $- 10$ $-10$
$0$ $0$ ........ $1$ $1$ ........ $0$ $0$ ............ $2$ $2$
$0$ $0$ ........ $0$ $0$ ........ $1$ $1$ ........ $- 5$ $-5$

$r_{1} = r_{1} - 2 r_{3}$ $r_1 = r_1 - 2r_3$
$1$ $1$ ........ $0$ $0$ ........ $0$ $0$ ........... $0$
$0$ ........ $1$ ........ $0$ ............ $2$
$0$ ........ $0$ ........ $1$ ........ $-5$

Science

Math

Humanities

... and beyond

How do you solve using gaussian elimination or gauss-jordan elimination, $y + z = - 3$ $y+z=-3$ , $x - y + z = - 7$ $x-y+z=-7$ , $x + y = 2$ $x+y=2$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve using gaussian elimination or gauss-jordan elimination, y+z=−3y+z=-3, x−y+z=−7x-y+z=-7, x+y=2x+y=2?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve using gaussian elimination or gauss-jordan elimination, $y + z = - 3$ $y+z=-3$ , $x - y + z = - 7$ $x-y+z=-7$ , $x + y = 2$ $x+y=2$ ?