Chapter C, Problem 1PP

To determine

Solve the given simultaneous equations using MATLAB.

Answer to Problem 1PP

The solutions for the simultaneous equations are $\underset{\_}{x_1=3,x_2=2,\text{and}{x}_3=3}$

Explanation of Solution

Calculation:

Consider the given equations.

$3x_1-x_2-2x_3=1$        (1)

$-x_1+6x_2-3x_3=0$        (2)

$-2x_1-3x_2+6x_3=6$        (3)

Write Equations (1), (2), and (3) in matrix form.

$\left[\begin{array}{ccc}3& -1& -2\\ -1& 6& -3\\ -2& -3& 6\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ 6\end{array}\right]$

Write the Matlab code to solve the given equations.

A= [3 -1 -2; -1 6 -3; -2 -3 6];

B=[1; 0; 6];

C=inv(A)*B

The output for the above program is given below.

C =

   3.0000

   2.0000

   3.0000

From the Matlab output, the values are,

$x_1=3,x_2=2,\text{and}{x}_3=3$.

Conclusion:

Thus, the solutions for the simultaneous equations are $\underset{\_}{x_1=3,x_2=2,\text{and}{x}_3=3}$.