Question

Solve the following equations by Gauss Jacobi’s Iteration method
15x + 2y + z = 18

2x + 20y − 3z = 19

3x − 6y + 25z = 22​

Answer 1

Answer:

x1=1.2

y1=0.95

z1=0.88

x2=1.015

y2=0.962

z2=0.964

Answer 2

Answer: $x=\frac{6}{5}$,  $y=\frac{19}{20}$ and  $z=\frac{22}{25}$.

Step-by-step explanation:

• Given:

        $15x+2y+z=18\\2x+20y-3z=19\\3x-6y+25z=22$

• To find: Value of x, y and z by Gauss Jacobi's method.
• Solution:

        $15x+2y+z=18$

   ⇒ $15x=18-2y-z$

   ⇒ $x=\frac{1}{15}[18-2y-z]$

Putting y=0 and z=0.

   ⇒ $x=\frac{18}{15}$

   ⇒ $x=\frac{6}{5}$

again,

       $2x+20y-3z=19$

   ⇒ $20y=19-2x+3z$

   ⇒ $y=\frac{1}{20}[19-2x+3z]$

Putting x=0 and z=0.

   ⇒ $y=\frac{19}{20}$

again,

       $3x-6y+25z=22$

   ⇒ $25z=22-3x+6y$

   ⇒ $z=\frac{1}{25}[22-3x+6y]$

Putting x=0 and y=0.

   ⇒ $z=\frac{22}{25}$

So,  $x=\frac{6}{5}$,  $y=\frac{19}{20}$ and  $z=\frac{22}{25}$.

• Hence, the required values are as above.

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