Use the theorem given below to show that if two rows of a square matrix are equal, then det A = 0. The same is true for two columns. Why? Let A be a square matrix. a. If a multiple of one row of A is added to another row to produce a matrix B, then det B = det A. b. If two rows of A are interchanged to produce B, then det B = - det A. c. If one row of A is multiplied by k to produce B, then det B = k det A.
Use the theorem given below to show that if two rows of a square matrix are equal, then det A = 0. The same is true for two columns. Why? Let A be a square matrix. a. If a multiple of one row of A is added to another row to produce a matrix B, then det B = det A. b. If two rows of A are interchanged to produce B, then det B = - det A. c. If one row of A is multiplied by k to produce B, then det B = k det A.
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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![Use the theorem given below to show that if two rows of a square matrix are equal, then det A = 0. The same is true for two columns.
Why?
Let A be a square matrix.
a. If a multiple of one row of A is added to another row to produce a matrix B, then det B = det A.
b. If two rows of A are interchanged to produce B, then det B = - det A.
c. If one row of A is multiplied by k to produce B, then det B = k det A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff96cdc2-7807-4421-a794-d30f1f1244f8%2Fefa22ba5-cc49-49ee-9998-c2548fa5c808%2Fpi7jj7w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use the theorem given below to show that if two rows of a square matrix are equal, then det A = 0. The same is true for two columns.
Why?
Let A be a square matrix.
a. If a multiple of one row of A is added to another row to produce a matrix B, then det B = det A.
b. If two rows of A are interchanged to produce B, then det B = - det A.
c. If one row of A is multiplied by k to produce B, then det B = k det A.
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