**ERIC Number:**EJ774898

**Record Type:**Journal

**Publication Date:**2007-Sep

**Pages:**7

**Abstractor:**Author

**Reference Count:**1

**ISBN:**N/A

**ISSN:**ISSN-0020-739X

A Strange Property of the Determinant of Minors

Ajibade, A. O.; Rashid, M. A.

International Journal of Mathematical Education in Science and Technology, v38 n6 p852-858 Sep 2007

If M[subscript ij] are minors of an n x n determinant D with elements a[subscript ij] (1 less than or equal to i,j less than or equal to n), then we prove the following relationship [vertical bar]M[subscript k][vertical bar] = [vertical bar]D[vertical bar][superscript k-1]delta[subscript k] where M[subscript k] is any square sub matrix of order k of the matrix of minors M, delta[subscript k] is the determinant of a submatrix of D of order (n - k) taking the complements of the "row/column" positions that was used in M[subscript k], and 1 less than or equal to k less than or equal to n. The above relation generalizes the trivial case for k = 1 and is consistent with the proven relationship for k = n when delta[subscript n] is taken as 1.

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A