Math Problem Statement
Consider an m×n matrix A such that every column of A contains either only zero elements or zero elements throughout except one which has the value unity. Show that every minor of A has either has the value 0 or ±1.
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Minors
Determinants
Permutation Matrices
Formulas
Determinant formula for permutation matrices
Minor determinant calculation
Theorems
Determinant of permutation matrices
Properties of standard basis vectors
Suitable Grade Level
Undergraduate Level