C3091327 - 27(Statement of the problem Proof Since A and B...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 27. (Statement of the problem.) Proof. Since A and B are symmetric, by the definition we have AT = A, B T = B. () "=" Suppose that AB = BA. Then (AB)T = (BA)T = AT B T (By Algebraic Rule 4 for Transpose) = AB (By (*) ) By definition of symmetry, AB is symmetric. "=" Suppose that AB is symmetric. Then AB= (AB)T (By definition of symmetry) (By Algebraic Rule 4 for Transpose) = B T AT = BA (By (*) ) That is, AB = BA. 1 ...
View Full Document

This note was uploaded on 04/01/2008 for the course MATH 309 taught by Professor Samiabdul during the Spring '08 term at Michigan State University.

Ask a homework question - tutors are online