Let A be a known nxn matrix, b be a known n-dimensional vector and z be an unknown vector defined by solutions of Ag = b. (a) Explain how to compute the determinant of the n xn matrix A. (b) What conditions must be satisfied by the matrix A such that the equation Ar = b has exactly one solution for the unknown vector r?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 11CC
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From practice sheet I need the solution For b)

Let A be a known n x n matrix, b be a known n-dimensional vector and z be an unknown
vector defined by solutions of Ar = b.
(a) Explain how to compute the determinant of the n x n matrix A.
(b) What conditions must be satisfied by the matrix A such that the equation Ar = b
has exactly one solution for the unknown vector r?
Transcribed Image Text:Let A be a known n x n matrix, b be a known n-dimensional vector and z be an unknown vector defined by solutions of Ar = b. (a) Explain how to compute the determinant of the n x n matrix A. (b) What conditions must be satisfied by the matrix A such that the equation Ar = b has exactly one solution for the unknown vector r?
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