Solution Found!
Use Theorem 3 (but not Theorem 4) to show that if two rows
Chapter 3, Problem 30E(choose chapter or problem)
Use Theorem 3 (but not Theorem 4) to show that if two rows of a square matrix A are equal, then det A = 0. he same is true for two columns. Why?Theorem 3Row OperationsLet 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 detB = det A.b. If two rows of A are interchanged to produce B, then detB D = det A.c. If one row of A is multiplied by k to produce B, then detB D k = det A.
Questions & Answers
QUESTION:
Use Theorem 3 (but not Theorem 4) to show that if two rows of a square matrix A are equal, then det A = 0. he same is true for two columns. Why?Theorem 3Row OperationsLet 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 detB = det A.b. If two rows of A are interchanged to produce B, then detB D = det A.c. If one row of A is multiplied by k to produce B, then detB D k = det A.
ANSWER:Solution 30EReasons for det =0, when there are two equal rows or columns:Let be a square matrix such that, either two rows are equal or two columns are equal.“If the equal two rows or columns are in