« Introduction to Determinant 

For linear system , if , then the system has the unique solution,
where is the matrix obtained by replacing the ith column of A by b.
Example 1:
Solve for the following system of linear equations by Cramer's rule,
Solution:
The coefficient matrix A and the vector b are
,
respectively. Then,
Thus, .
Triangle:
Consider the triangle with vertices and .
The area of the triangle is
.
Example 2:
Compute the area of the triangle with vertices and .
Solution:
The area is
.
Parallelogram:
Suppose we have a parallelogram with vertices , and ,
Then, the area of the parallelogram is