# algebra-Determinant

May 28th, 2015
Studypool Tutor
Price: \$10 USD

Tutor description

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of linear equations has a unique solution iff the determinant of the

Word Count: 1146
Showing Page: 1/8
Algebra>Linear Algebra>Determinants>MathWorld Contributors>Budney>Interactive Entries>Interactive Demonstrations>DeterminantDeterminants are mathematical objects that are very useful in the analysis and solution ofsystems of linear equations. As shown byCramer's rule, a nonhomogeneous system of linear equations has a unique solutioniffthe determinant of the system'smatrixisnonzero(i.e., thematrixis nonsingular). For example, eliminating,, andfrom the equations(1)(2)(3)gives the expression(4)which is called the determinant for this system of equation. Determinants are defined only forsquare matrices.If the determinant of amatrixis 0, thematrixis said to besingular, and if the determinant is 1, the matrix is said to beunimodular.The determinant of amatrix,(5)is commonly denoted,, or in component notation as,, or(Muir 1960, p.17). Note that the notationmay be more convenient when indicating the absolute value of a determinant, i.e.,instead of. The determinant is implemented inMathematicaasDet[m].Adeterminant is defined to be(6)Adeterminant can be expanded "byminors" to obtain(7)A general determinant for amatrixhas a value(8)with no implied summation overand where(also denoted) is thecofactorofdefined by(9)andis theminorofmatrixformed by eliminating rowand columnfrom. This process

## Review from student

Studypool Student
" Excellent work as always thanks so much "

1826 tutors are online

### Other Documents

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors