xercise 8.5.3. Check that the well known formula for the determinant of a 2 × 2 matrix, det tisfies the three properties of Definition 8.2.1 and thus is a correct formula for the determinant. Definition 8.2.1. A function Mat→ R is said to a determinant if is satisfies the following three properties: (i) det(I) = 1. (ii) det(EA) = -det(A) if E represents the elementary row operation which swaps two rows. (iii) The determinant is linear with respect to a single row: -4-0-0 det avi + Bwi = adet + Bdet Un
xercise 8.5.3. Check that the well known formula for the determinant of a 2 × 2 matrix, det tisfies the three properties of Definition 8.2.1 and thus is a correct formula for the determinant. Definition 8.2.1. A function Mat→ R is said to a determinant if is satisfies the following three properties: (i) det(I) = 1. (ii) det(EA) = -det(A) if E represents the elementary row operation which swaps two rows. (iii) The determinant is linear with respect to a single row: -4-0-0 det avi + Bwi = adet + Bdet Un
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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![Exercise 8.5.3. Check that the well known formula for the determinant of a 2 × 2 matrix,
det ([$])
satisfies the three properties of Definition 8.2.1 and thus is a correct formula for the determinant.
Definition 8.2.1. A function Mat → R is said to a
determinant if is satisfies the following three properties:
(i) det(I) = 1.
(ii) det(EA) = −det(A) if E represents the elementary
row operation which swaps two rows.
(iii) The determinant is linear with respect to a single row:
det
V1
αυ; + βω;
Vn
= adet
+ Bdet
Wi
Vn](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80d412e1-3977-44a4-94cf-90c8aaabb7a1%2Fa2ad3f4b-0909-4446-a520-0ff7b545653b%2Fbe4eeds_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 8.5.3. Check that the well known formula for the determinant of a 2 × 2 matrix,
det ([$])
satisfies the three properties of Definition 8.2.1 and thus is a correct formula for the determinant.
Definition 8.2.1. A function Mat → R is said to a
determinant if is satisfies the following three properties:
(i) det(I) = 1.
(ii) det(EA) = −det(A) if E represents the elementary
row operation which swaps two rows.
(iii) The determinant is linear with respect to a single row:
det
V1
αυ; + βω;
Vn
= adet
+ Bdet
Wi
Vn
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