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Student[LinearAlgebra]

 Minor
 compute a minor of a Matrix

 Calling Sequence Minor(A, r, c, options)

Parameters

 A - Matrix r - integer; row to omit c - integer; column to omit options - (optional) parameters; for a complete list, see LinearAlgebra[Minor]

Description

 • The Minor(A, r, c) command, where A is an $mxm$ (square) Matrix, returns the determinant of the $\left(m-1\right)x\left(m-1\right)$ submatrix found by omitting the rth row and the cth column of A.

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{LinearAlgebra}}\right):$
 > $A≔⟨⟨a|b|c⟩,⟨d|e|f⟩,⟨g|h|i⟩⟩$
 ${A}{≔}\left[\begin{array}{ccc}{a}& {b}& {c}\\ {d}& {e}& {f}\\ {g}& {h}& {i}\end{array}\right]$ (1)
 > $\mathrm{Minor}\left(A,3,3\right)$
 ${a}{}{e}{-}{b}{}{d}$ (2)
 > $B≔⟨⟨1,2,3,-4⟩|⟨5,6,-7,8⟩|⟨9,-10,11,12⟩|⟨-13,14,15,16⟩⟩$
 ${B}{≔}\left[\begin{array}{cccc}{1}& {5}& {9}& {-13}\\ {2}& {6}& {-10}& {14}\\ {3}& {-7}& {11}& {15}\\ {-4}& {8}& {12}& {16}\end{array}\right]$ (3)
 > $\mathrm{Minor}\left(B,2,3\right)$
 ${-720}$ (4)