Math Calculators, Lessons and Formulas

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« Introduction to Determinant
Determinants: (lesson 2 of 2)

Applications of Determinants

Cramer's rule:

For linear system Applications of Determinants, if Cramer's rule, then the system has the unique solution,

Applications of Determinants

where Cramer's rule is the matrix obtained by replacing the i-th column of A by b.

Example 1:

Solve for the following system of linear equations by Cramer's rule,

Applications of Determinants


The coefficient matrix A and the vector b are

Applications of Determinants,

respectively. Then,

Cramers rule

Thus, Cramers rule.



Consider the triangle with vertices Triangle area and Triangle area.

Triangle area

The area of the triangle is

Triangle area.

Example 2:

Compute the area of the triangle with vertices Triangle area example and Triangle area example.


The area is

Triangle area solution.


Suppose we have a parallelogram with vertices Parallelogram area, Parallelogram area and Parallelogram area,

Parallelogram area example

Then, the area of the parallelogram is

Parallelogram area example