How do you find inverse of the matrix using augmented matrix?

Answer 1

your first step is to augment(connect with the bar in between) the identity matrix onto the right side of the original matrix

then your main objective is to turn your original matrix into the identity matrix while only using elementary row operations

elementary row operation rules:

1. row swap- you can swap any row with another row. meaning the entire first row can be swapped with the second, or third row but only entire rows may be swapped
2. row multiplication- you can multiply or divide entire rows by a constant ex: if row1=3t-5s then row1 x 2=6t-10s (note you must multiply every term in the variable)
3. row addition- any row can be added or subtracted onto another row to change that row. note if you were to add row1 to row2 for example change would only be done to row2 not row1. (very important)- be careful when adding rows remember that when rows are being added/subtracted, they subtract according to how columns within rows align with. this is where the most mistakes happen.
4. (most important)- what ever action you perform on a row you do it to the entire row. you must treat both sides of the line as ONE UNIT(thasshow i remembered). when you perform an operation on the original matrix, you cannot forget to do the same to the augmented peice

if the original matrix is sucessfully changed into the identity matrix using these rules, then you should end up with the identity matrix on the original side and theinverse matrix on the augmented side

examples of this method can be found by looking up linear algebra on khanacadamy.org