Method 1&2 Graphical method and Cramer's Rule
There are several methods appropriate for solving
small (n 3) sets of simultaneous equations
Method 1: Graphical method
This method is to draw the equation's line then
find the interception points.
We won't show it here.
Method 2: Cramer's Rule
These equations will be solved by using different methods
later.
Step 1: Express the equation in matrix form.
Step 2: Find the determinant of [A]
Step 3: Find the determinant of xi, i = 1, 2, 3
To define [xi], replace the 'i' column of [A] to [B], the other column is same with [A]
Step 4: Find xi by
CLO2 Linear eqns with multiple variables solving Page 1
, Method 3: Gauss Elimination
Method 3: Gauss Elimination
There are two phases of Gauss Elimination
• Forward Elimination
• Back substituting
Step 1: Forward Elimination
Step 1.1: Express the equation in matrix form.
Step 1.2: Row 3 of [A] and [B] - a31/a11 * Row 1 of [A] and [B]. This step is to make a31 = 0.
Step 1.3: Row 2 - a21/a11 * Row 1. This step is to make a21 = 0.
Step 1.3: Row 3 - a32'/a22' * Row 2. This step is to make a32 = 0. (a32' and a22' are the new a after step 1.2 and step 1.3)
Now, we have completed forward elimination, our matrix now is
Step 2: Back substituting
Step 2.1: Multiply Row 3 of [A] with {x}.
We can get 5.3519*x3 = -32.1111, then we can solve for x3.
x3 = -32.1111/5.3519 = -6
Step 2.2: Multiply Row 2 of [A] with {x}.
We can get -5.4*x2 + 1.7*x3 = -53.4, we know that x3 = -6
then we can solve for x2
x2 = (-53.4 - 1.7*-6)/-5.4 = 8
Step 2.3: Multiply Row 1 of [A] with {x}.
We can get 10*x1 + 2*x2 - *x3 = 27, we know that x2 = 8 and
CLO2 Linear eqns with multiple variables solving Page 2
There are several methods appropriate for solving
small (n 3) sets of simultaneous equations
Method 1: Graphical method
This method is to draw the equation's line then
find the interception points.
We won't show it here.
Method 2: Cramer's Rule
These equations will be solved by using different methods
later.
Step 1: Express the equation in matrix form.
Step 2: Find the determinant of [A]
Step 3: Find the determinant of xi, i = 1, 2, 3
To define [xi], replace the 'i' column of [A] to [B], the other column is same with [A]
Step 4: Find xi by
CLO2 Linear eqns with multiple variables solving Page 1
, Method 3: Gauss Elimination
Method 3: Gauss Elimination
There are two phases of Gauss Elimination
• Forward Elimination
• Back substituting
Step 1: Forward Elimination
Step 1.1: Express the equation in matrix form.
Step 1.2: Row 3 of [A] and [B] - a31/a11 * Row 1 of [A] and [B]. This step is to make a31 = 0.
Step 1.3: Row 2 - a21/a11 * Row 1. This step is to make a21 = 0.
Step 1.3: Row 3 - a32'/a22' * Row 2. This step is to make a32 = 0. (a32' and a22' are the new a after step 1.2 and step 1.3)
Now, we have completed forward elimination, our matrix now is
Step 2: Back substituting
Step 2.1: Multiply Row 3 of [A] with {x}.
We can get 5.3519*x3 = -32.1111, then we can solve for x3.
x3 = -32.1111/5.3519 = -6
Step 2.2: Multiply Row 2 of [A] with {x}.
We can get -5.4*x2 + 1.7*x3 = -53.4, we know that x3 = -6
then we can solve for x2
x2 = (-53.4 - 1.7*-6)/-5.4 = 8
Step 2.3: Multiply Row 1 of [A] with {x}.
We can get 10*x1 + 2*x2 - *x3 = 27, we know that x2 = 8 and
CLO2 Linear eqns with multiple variables solving Page 2
