Use GaussJordan row reduction to solve the given system of e

Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where

y = y(x)

and

z = z(x).)

Solution

Given

-2x/5 +y -3z/5=0
-3x/5 -2y/5 +z =0
x -3y/5 -2z/5=0

multiplying both sides by 5 in all equations

-2x +5y -3z=0
-3x -2y +5z =0
5x -3y -2z=0

we write it in matrix form

-2       5      -3        0        // we have to make the first element of the matri equal to 1

-3     -2        5        0

5      -3      -2        0

now we have to reduce it

R3->R3 +2R1

-2       5      -3        0

-3     -2        5        0

1       7       -8        0

R1 ->R1+3R3

1       26      -27        0

-3     -2        5        0

1       7       -8        0

R2->R2 +3R1          R3->R3-R1

1       26      -27        0

0      76       -76        0

0      -19       19        0

R3->R3-(1/4)*R2

1       26      -27        0

0      76       -76        0

0        0        0         0

now we get

x +26y -27z =0         (1)

76y - 76z =0         => y=z             (2)

from (1) and (2)

x+26y -27y =0

x-y=0

x=y

therefore

y=x

and z=x