Solution Found!
Show that AIn= A when A is an m × n matrix. [Hint: Use the
Chapter 2, Problem 32E(choose chapter or problem)
QUESTION:
Show that \(A I_{n}=A\) when A is an \(m \times n\) matrix. [Hint: Use the (column) definition of \(A I_{n}\)].
Questions & Answers
QUESTION:
Show that \(A I_{n}=A\) when A is an \(m \times n\) matrix. [Hint: Use the (column) definition of \(A I_{n}\)].
ANSWER:Solution
Step 1
Let us assume A be a matrix of order m x n.
Suppose A be a matrix of order m x n with row ai1 , ai2 ,ai3 ………,ai n and In be a identity matrix.
Now, Assume x In = x for all x in ℝn then
(i , j) of x In= (row ith of x)(column jth of In)
= [ xi1 , xi2 ,xi3 ………,xi n][ 0 , ........0 , 1 , 0 , .........., 0 ]