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

Solution:

The coefficient matrix A and the vector b are

Applications of Determinants,

respectively. Then,

Cramers rule

Thus, Cramers rule.

Areas:

Triangle:

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.

Solution:

The area is

Triangle area solution.

Parallelogram:

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