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Problem 7: Let 8: M2x2(F) → F be a function which has the following three properties: i.) 6 is linear in each row of the matrix when the other row is fixed. ii.) If A has identical rows, then 8(A) = 0 iii.) 8(1₂) = 1. Prove that is the determinant function.

Problem 7: Let 8: M2x2(F) → F be a function which has the following three properties: i.) 6 is linear in each row of the matrix when the other row is fixed. ii.) If A has identical rows, then 8(A) = 0 iii.) 8(1₂) = 1. Prove that is the determinant function.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 7: Let 8 : M2×2(F) → F be a function which has the following three properties: i.) 8 is linear in each row of the matrix when the other row is fixed. ii.) If A has identical rows, then (A) = 0 iii.) 8(1₂) = 1. Prove that is the determinant function.
Transcribed Image Text:Problem 7: Let 8 : M2×2(F) → F be a function which has the following three properties: i.) 8 is linear in each row of the matrix when the other row is fixed. ii.) If A has identical rows, then (A) = 0 iii.) 8(1₂) = 1. Prove that is the determinant function.
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