6.* Suppose that A = [aj] is a 3 x 3 matrix whose entries are equal to either0, 1, or 2, namely aij e {0,1, 2} for every i, j e {1,2,3}. Suppose that Ais invertible, and write A-1 = [bj]. Explain why, for i,j e {1,2,3}, bij isa rational number of the form k/2' or -k/2' for some positive integers k, l(depending on i, j).

The given matrix is A=aij of order 3×3 whose entries are equal to either 0, 1 or 2. i.e. aij∈0,1,2 ∀…

6.* Suppose that A = [aj] is a 3 x 3 matrix whose entries are equal to either 0, 1, or 2, namely aij e {0,1, 2} for every i, j e {1,2, 3}. Suppose that A is invertible, and write A- = [b;]. Explain why, for i,je {1,2,3}, b;j is a rational number of the form k/2' or –k/2' for some positive integers k, l (depending on i, j).

6.* Suppose that A = [aj] is a 3 x 3 matrix whose entries are equal to either 0, 1, or 2, namely aij e {0,1, 2} for every i, j e {1,2, 3}. Suppose that A is invertible, and write A- = [b;]. Explain why, for i,je {1,2,3}, b;j is a rational number of the form k/2' or –k/2' for some positive integers k, l (depending on i, j).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 3AEXP

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