Chapter 1.4 ElementaryMatrices

# 3 add 2 times row 1 to row 3 add 2 times row 1 to row

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: times row 1 to row 3. 1 Interchange rows 2 and 3. Multiply row 2 by . You end up 3 with I3 . Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Properties of an Invertible Matrix Theorem If A is an n × n matrix, then the following are equivalent. (a) A is invertible. (b) Ax = 0 has only the trivial solution. (c) rref (A) = In . (d) A = E1 E2 . . . Er for some elementary matrices E1 , E2 , . . . , Er . Proof. (a) ⇒ (b): (b) ⇒ (c): (c) ⇒ (d): (d) ⇒ (a): Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Row Equivalent Matrices If a matrix B can be obtained from a matrix A by a ﬁnite sequence of elementary row operations, then A can be obtained from B with the reverse sequence of the inverse elementary row operations. We say A and B are row equivale...
View Full Document

Ask a homework question - tutors are online