9 ible matrix, prove that 5A is an invertible matrix.[³].= b₁,e sameis the(a) byb4].and DIn Exercises 9 and 10, mark each statement True or False. Justifyeach answer.9. a In order for a matrix B to be the inverse of A, bothequations AB = I and BA = I must be true.b. If A and B are n x n and invertible, then ATB¹ is theinverse of AB.a- [ºc. If A =e.10. /a.blik 8X1101+10bdand ab-cd #0, then A is invertible.d. If A is an invertible n x n matrix, then the equationAx=b is consistent for each b in R".Each elementary matrix is invertible.A product of invertible n x n matrices is invertible, andthe inverse of the product is the product of their inversesin the same order.c. If A =b. If A is invertible, then the inverse of AT is A itself.= [a b]dand ad bc, then A is not invertible.=d. If A can be row reduced to the identity matrix, then A mustbe invertible. DMod2.20e. If A is invertible, then elementary row operations thatreduce A to the identity I, also reduce A-¹ to In.11. Let A be an invertible n x n matrix, and let B be an n x pmatrix. Show that the equation AX = B has a unique solu-tion AB.12. Let A be an invertible n x n matrix, and let B be an n x p ma-trix. Explain why A¹B can be computed by row reduction:

each answer. 9. a In order for a matrix B to be the inverse of A, both equations AB = I and BA = I must be true. b. If A and B are n x n and invertible, then ATB¹ is the inverse of AB. b - [a 2] d d. If A is an invertible n x n matrix, then the equation Ax = b is consistent for each b in R". e. Each elementary matrix is invertible. c. If A = and and ab-cd0, then A is invertible. is invertible and

each answer. 9. a In order for a matrix B to be the inverse of A, both equations AB = I and BA = I must be true. b. If A and B are n x n and invertible, then ATB¹ is the inverse of AB. b - [a 2] d d. If A is an invertible n x n matrix, then the equation Ax = b is consistent for each b in R". e. Each elementary matrix is invertible. c. If A = and and ab-cd0, then A is invertible. is invertible and

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section2.1: Matrices And Vectors

Problem 7P

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