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 & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 58E
Related questions
Question
Please solve max in 60 minutes and no reject thank u about
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).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning