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In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the vector of right hand sides of the equations. The Cramer's rule for 3 equations and 3 unknows is as follows: Cramer's Rule for Three Equations in Three Unknowns The solution to the system a?x + b?y + c?z = d? a?x + b?y + c?z = d? a?x + b?y + c?z = d? is given by x = \frac{D_x}{D}, y = \frac{D_y}{D}, and z = \frac{D_z}{D}, where $\begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}$, $D_x = \begin{vmatrix} d_1 & b_1 & c_1 \\ d_2 & b_2 & c_2 \\ d_3 & b_3 & c_3 \end{vmatrix}$, $D_y = \begin{vmatrix} a_1 & d_1 & c_1 \\ a_2 & d_2 & c_2 \\ a_3 & d_3 & c_3 \end{vmatrix}$, $D_z = \begin{vmatrix} a_1 & b_1 & d_1 \\ a_2 & b_2 & d_2 \\ a_3 & b_3 & d_3 \end{vmatrix}$, provided that D ? 0. Next, using three different methods, you will write a Matlab scrip to solve the following system of linear equations: 3x + 4y + 6z = 1 x - 2y + 7z = 10 2x + 3y - 9z = 15 Task 1: Use the left division operator to find the solution vector (x,y,z). Task 2: Write a custom function called Cramer_rule(A,b) to find the vector x in Ax=b. Task 3: Use the custom function you wrote to find the solution vector (x,y,z) for the above linear equations. Task 4: Use Gaussian elimination to find the solution vector (x,y,z). Task 5: Use Gauss-Jordan elimination to find the solution vector (x,y,z).

          In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear
equations with as many equations as unknowns, valid whenever the system has a unique
solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix
and of matrices obtained from it by replacing one column by the vector of right hand sides of the
equations. The Cramer's rule for 3 equations and 3 unknows is as follows:
Cramer's Rule for Three Equations in Three Unknowns
The solution to the system
a?x + b?y + c?z = d?
a?x + b?y + c?z = d?
a?x + b?y + c?z = d?
is given by x = \frac{D_x}{D}, y = \frac{D_y}{D}, and z = \frac{D_z}{D}, where
$\begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}$, $D_x = \begin{vmatrix} d_1 & b_1 & c_1 \\ d_2 & b_2 & c_2 \\ d_3 & b_3 & c_3 \end{vmatrix}$,
$D_y = \begin{vmatrix} a_1 & d_1 & c_1 \\ a_2 & d_2 & c_2 \\ a_3 & d_3 & c_3 \end{vmatrix}$, $D_z = \begin{vmatrix} a_1 & b_1 & d_1 \\ a_2 & b_2 & d_2 \\ a_3 & b_3 & d_3 \end{vmatrix}$,
provided that D ? 0.
Next, using three different methods, you will write a Matlab scrip to solve the following system
of linear equations:
3x + 4y + 6z = 1
x - 2y + 7z = 10
2x + 3y - 9z = 15
Task 1: Use the left division operator to find the solution vector (x,y,z).
Task 2: Write a custom function called Cramer_rule(A,b) to find the vector x in Ax=b.
Task 3: Use the custom function you wrote to find the solution vector (x,y,z) for the above linear
equations.
Task 4: Use Gaussian elimination to find the solution vector (x,y,z).
Task 5: Use Gauss-Jordan elimination to find the solution vector (x,y,z).

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear
equations with as many equations as unknowns, valid whenever the system has a unique
solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix
and of matrices obtained from it by replacing one column by the vector of right hand sides of the
equations. The Cramer's rule for 3 equations and 3 unknows is as follows:
Cramer's Rule for Three Equations in Three Unknowns
The solution to the system
a?x + b?y + c?z = d?
a?x + b?y + c?z = d?
a?x + b?y + c?z = d?
is given by x = (Dx)/(D), y = (Dy)/(D), and z = (Dz)/(D), where
a1 b1 c1
a2 b2 c2
a3 b3 c3, Dx = d1 b1 c1
d2 b2 c2
d3 b3 c3,
Dy = a1 d1 c1
a2 d2 c2
a3 d3 c3, Dz = a1 b1 d1
a2 b2 d2
a3 b3 d3,
provided that D ? 0.
Next, using three different methods, you will write a Matlab scrip to solve the following system
of linear equations:
3x + 4y + 6z = 1
x - 2y + 7z = 10
2x + 3y - 9z = 15
Task 1: Use the left division operator to find the solution vector (x,y,z).
Task 2: Write a custom function called Cramerrule(A,b) to find the vector x in Ax=b.
Task 3: Use the custom function you wrote to find the solution vector (x,y,z) for the above linear
equations.
Task 4: Use Gaussian elimination to find the solution vector (x,y,z).
Task 5: Use Gauss-Jordan elimination to find the solution vector (x,y,z).

Added by Purificaci-N M.

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