##### Like what you saw?

##### Create FREE Account and:

- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics

# The Inverse of a Square Matrix - Problem 2

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

Let's find the inverse of another 2 by 2 matrix. Here I have matrix A which is -2 3, -4 6. I want to find the inverse. Remember the first step is to create an augmented matrix that starts with matrix A -2 3, -4 6. Then you augment it with the identity matrix 1 0, 0 1.

The idea here is, you want to do row operations on this augmented matrix, until you can get the identity matrix on the left. Then whatever is on the right is your inverse. So you want to change this to a 1. Change this to a 0. This to a 0. This to a 1 through row operations. So my idea here is I'm going to try to change this entry to 0. I'm going to do that by multiplying the top row by -2, and adding it to the bottom row. The notation for that is -2 times row 1 plus row 2.

The row number you end with, that's the row that's going to get changed. So I'm going to leave the top row alone -2 3, 1, 0. Then -2 times -2 is 4, plus 4 -4, 0. -2 times 3 is -6 plus 6 is 0. -2 times 1 is -2 plus 0, -2. -2 times 0 is 0, plus 1 is 1.

Now we've got a problem. I mean I did manage to get this first entry in the bottom row to be 0, but I didn't want a 0 here. I wanted to end up with a 1 here. Now that I have a 0, there is no way to actually get a 1 there.

So this means that this matrix is not invertible. The matrix I started with A is not invertible. Now if you look at it, the bottom row is actually 2 times the top row. Whenever one row is a constant multiple of the other, the matrix is not going to be invertible. So A has no inverse. Later on we'll talk about a quicker way finding out if a matrix is invertible using determinants.

Please enter your name.

Are you sure you want to delete this comment?

###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

Thiswas EXCELLENT! I am a math teacher and have been looking for an easy/logical way to explain the lateral area of a cone to my students and this was incredibly helpful, thank you very much!”

I just learned more In 3 minutes of polygons here than I do in 3 weeks in my math class”

Hahaha, his examples are the same problems of my math HW!”

###### Get Peer Support on User Forum

Peer helping is a great way to learn. Join your peers to ask & answer questions and share ideas.

##### Concept (1)

##### Sample Problems (3)

Need help with a problem?

Watch expert teachers solve similar problems.

## Comments (0)

Please Sign in or Sign up to add your comment.

## ·

Delete