Find the inverse of A=4 2 using reduced row echlon technique.This is a 2x2 matri

Question

Find the inverse of A=4 2 using reduced row echlon technique.This is a 2x2 matrix i just dont know how                                  3 1 how to put it in brackets on this software.anyway i need somehelp with the steps of echelon form to find an inverse im just notsure what the steps are. please help will rate! Find the inverse of A=4 2 using reduced row echlon technique.This is a 2x2 matrix i just dont know how                                  3 1 how to put it in brackets on this software.anyway i need somehelp with the steps of echelon form to find an inverse im just notsure what the steps are. please help will rate!

Explanation / Answer

Since this is a 2x2 matrix the easiest way to find the inverseis to swap the entries on the main diagonal and make the offdiagonal entries negative. Then scale the resulting matrix by1/det(a). Since they want you to use the reduced row echelon form, bythe invertible matrix theorem, if a matrix is invertible it is alsorow equivalent to the nxn identity matrix. Because of this,any operations done to reduce A to the identity also reduce theidentity to A-1. Augment a matrix [A I] and reduce it to where each pivot has0's above and below it. In general that's what a reduced rowechelon form looks like.

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