Question

Solve by gaussian method

x-y=-1

x-z=-6

6x-2y-3z=-18

Answer 1

Answer:-

By the gaussian the solution of the given system of equations is

x=2 , y= 3 and z=8

Solution:-

We have given the equations

x-y=-1

x-z=-6

6x-2y-3z=-18

These system of equations has agumented matrix as

Now performing row operations to get the matrix in row-echelon form.

It means change Row 2 to Row 2 –Row1 and change Row3 to Row3–6Row1.

Now change Row 3 to Row3–4Row2,

This gives the equations as

x-y=-1 ......(1)

y -z=-5 .....(2)

z=8 ......(3)

On putting the value of z in equatioe 2,we get

y-8=-5

Or y= -5+8

Or y= 3 ....(4)

On putting the value of y in equation 1,we get

x -3=-1

Or x= -1+3

Or x=2 ...........(5)

From equations 3,4 and 5, we get the solution as

x=2, y=3 and z=8

Hence, by the gaussian the solution of the given system of equations is

x=2 , y= 3 and z=8