(a) Suppose that B and C are invertible 4 × 4 matrices satisfying the following: • Columns 1 and 2 of B-¹ are, respectively, 2 -2 1. -2 - and = 3 -2 .Rows 3 and 4 of C-1 are, respectively, [o - - -2 0 1] and [1 1 −1 −1]. If X BC, find the (3, 1)-entry of X-¹ and the (2, 4)-entry of (XT)−¹. Explain your answers fully. (b) Let A and B be n × n matrices, and let y be a non-zero vector in R”. Show that if A - B is invertible, then the equations Ax=y and Bx = y do not have a common solution x ER". Hint: Suppose that x is some solution to both equations, and aim for a contradiction.

(a) Suppose that B and C are invertible 4 × 4 matrices satisfying the following: • Columns 1 and 2 of B-¹ are, respectively, 2 -2 1. -2 - and = 3 -2 .Rows 3 and 4 of C-1 are, respectively, [o - - -2 0 1] and [1 1 −1 −1]. If X BC, find the (3, 1)-entry of X-¹ and the (2, 4)-entry of (XT)−¹. Explain your answers fully. (b) Let A and B be n × n matrices, and let y be a non-zero vector in R”. Show that if A - B is invertible, then the equations Ax=y and Bx = y do not have a common solution x ER". Hint: Suppose that x is some solution to both equations, and aim for a contradiction.

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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