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Theorem 3. Let A be any n x n matrix. (a) If A' is the resulting matrix when the single row A is multiplied by the constant k, then det(A) = k sec(A). (b) If A' is the resulting matrix when two rows of A are interchanged, then det(A')=-det(A). (c) If A' is the resulting matrix when a multiple of one row A is added to another row, then det(A')=det(A).

Theorem 3. Let A be any n x n matrix. (a) If A' is the resulting matrix when the single row A is multiplied by the constant k, then det(A) = k sec(A). (b) If A' is the resulting matrix when two rows of A are interchanged, then det(A')=-det(A). (c) If A' is the resulting matrix when a multiple of one row A is added to another row, then det(A')=det(A).

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Please solve max in 60 minutes and no reject thank u about Linear algebra elementer

Prove the following theorem. An example of proof can be seen in the picture, maybe it can help you

Theorem 3. Let A be any n x n matrix.

(a) If A' is the resulting matrix when the single row A is multiplied by the constant k, then det(A) = k sec(A).

(b) If A' is the resulting matrix when two rows of A are interchanged, then det(A')=-det(A).

(c) If A' is the resulting matrix when a multiple of one row A is added to another row, then det(A')=det(A).

A = ann -- aan 0 ... det(A) 0 anrl 0 det(A) = aa . ann +a12 . (0) + a-n .. (0) + a,n . (0) – (0).ain - (0)ana1 %3D - (0).a1:- an(0). a2 det(A) = aa-. a nn
Transcribed Image Text:A = ann -- aan 0 ... det(A) 0 anrl 0 det(A) = aa . ann +a12 . (0) + a-n .. (0) + a,n . (0) – (0).ain - (0)ana1 %3D - (0).a1:- an(0). a2 det(A) = aa-. a nn
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