Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 10 - Section 10.5 - Inverses of Matrices and Matrix Questions - 10.5 Exercises - Page 731: 1

Answer

(a) identity (b) A, A (c) inverse

Work Step by Step

The identity matrix $I_{n}$ is the $n\times n$ matrix whose main diagonal entries are all 1 and whose other entries are all $0$. If $A$ is an $m\times n$ matrix, then $AI_{n}=A$ and $I_{m}A=A$ If $A$ is an $n\times n$ matrix, then the inverse of $A$ is the $n\times n$ matrix $A^{-1}$ with the following properties: $A^{-1}A=I_{n}$ and $AA^{-1}=I_{n}$ --- Fill the blanks with : (a) identity (b) A, A (c) inverse
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