Statements (44)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical theorem
|
| gptkbp:appliesTo |
homogeneous systems
linear_equations |
| gptkbp:basedOn |
properties of determinants
|
| gptkbp:can_be |
systems of equations
|
| gptkbp:hasDepartment |
n equations with n unknowns
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cramer's Rule
|
| gptkbp:is_a_time_for |
finding determinants
finding unknowns solving algebraic equations solving simultaneous equations |
| gptkbp:is_available_in |
det(A) = 0
the system has a unique solution |
| gptkbp:is_evaluated_by |
x_i = det(A_i) / det(A) for i = 1, 2, ..., n
|
| gptkbp:is_involved_in |
matrix methods
|
| gptkbp:is_located_in |
the 18th century
|
| gptkbp:is_used_in |
engineering problems
computer algorithms linear_algebra |
| gptkbp:previousName |
gptkb:Gabriel_Cramer
|
| gptkbp:provides |
solution for variables
|
| gptkbp:related_to |
matrix inversion
linear_transformations |
| gptkbp:requires |
square matrix
|
| gptkbp:suitableFor |
economics
physics statistics |
| gptkbp:taught |
mathematics courses
|
| gptkbp:technique |
can be computationally intensive
can be used for theoretical proofs can be visualized using geometric interpretations is foundational in understanding matrix theory is less efficient for large systems is often compared to other methods is sometimes used in computer graphics is sometimes used in control theory is sometimes used in data analysis is sometimes used in machine learning is sometimes used in operations research is sometimes used in optimization problems is straightforward for small systems is useful in teaching concepts of linear algebra requires calculation of determinants |
| gptkbp:uses |
determinants
|