Hi guys
I came across this Inverse of matrices by reduction question and need you help.
Find the inverse of the matrix A= [row1(1 2) row2(5 3)] and use it to solve { x+2y=7, 5x+3y=28 ??????
What you have to do is augment A to the identity matrix ( [A | I ] ) and then use elementary row operations until you turn A in to I. By doing these row operation on I in the same order you preformed them on A you will end up with the inverse of A (that is [A | I] turns in to [I | A^-1] after using elementary row operations.) Then you can use the inverse to solve the system (turn the system in to its matrix form then multiply both sides by the inverse). I hope that made sense (and helps).
Okay so you have a 2X2 matrix. to reduce that in to the identity you want to get 1's on the diagonals and zero's everywhere else. We can use row operation III (add a multiple of one row to another) to get turn the first entry of the second row to zero by adding -5 times the first row to the second. This elminates the 5 from the second row and turns the 3 in to a -7. Then you can use row operation II (multiply a row by a scalar) to turn the -7 in to a 1. Now we have 1's on the diagonal and only one other non zero entry, all we need to do is get rid of the 2 in the first row. We do this by using row operation III again and add -2 times the second row to the first. This should give you the identiy. So by preforming those exact operations on the identity you should obtain A inverse.