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## Linear algebra

### Course: Linear algebra>Unit 2

Lesson 5: Finding inverses and determinants

# Example of finding matrix inverse

Example of calculating the inverse of a matrix. Created by Sal Khan.

## Want to join the conversation?

• how we can fined the inverse of a matrices of LU decomposition?
• What would you do if matrix A didn't begin with 1? How would you transform it to the identity matrix?
• Assuming it doesn't begin with 0, divide every value in the augmented matrix's first row by the first number to get 1. Then, without actually changing the first row, take the first row multiplied by the negative of the first value of a row below it, and add it to that row, so that every value under the first 1 is a zero. Repeat this process for the second element in the second row, the third in the third row, and so on. When you get to the last element of the last row, start this process backwards so that the values above become 0s until you have the identity matrix.
• What does he say at ? Row etch-a-long form? What is "row etch-a-long form"?

Thanks,
• He says 'row echelon form.' Put any lines of all zeros on the bottom of the matrix, make the first entry in each row a one, and each entry in each row to the right of the first entry in the row above it. In form it is easy to see the solution to the equation.
• What do you do if the matrix starts with 0?
• If the top-left entry of the matrix is 0, you swap the top row with the bottom row (or whichever row is lowest down and has a non-zero first entry).
• Is it even possible to find inverse for a 5x5 matrix by the ref?
• A bit late, but sure, why wouldn't it be possible?
• You say in the beginning of the video that we know this matrix has the identy matrix when we get A to rref. Do we always have to check if a matrix has the Identity Matrix in the rref before we find the Inverse Matrix?
• nevermind, You'll of course find out in the process...
• Determining the equation of a line perpendicular to another
(1 vote)
• I keep on messing up my inverses, and the only change I do from other ways is I use R1 - R2, rather than -1 X R1 + R2. Is there a problem with that?
(1 vote)
• They aren't the same, but both can be used to replace R1, or R2, if that helps reduce the matrix.
(1 vote)
• Is this the only way to reduce to find the inverse. I am not talk about a different method but I mean is there only on possible inverse for each Matrix if there is an inverse.