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### Course: Algebra (all content)>Unit 20

Lesson 12: Introduction to matrix inverses

# Intro to matrix inverses

Sal introduces the concept of an inverse matrix. Created by Sal Khan.

## Want to join the conversation?

• Is there ever a matrix that does not have an existing inverse?
• Concur: determinant of 0 nullifies(???) an inverse of a matrix.
• So the absolute value sign around the A in this example is just for notation, right? It doesn't actually mean what it would with traditional absolute value?
• Good guess, The notation used for determinants is no way related to the absolute value. The value of a determinant is a real number, which means negative values are also possible
• this all seems very odd to me, if a matrix is used to order data, how come multiplying and devising like this is the best way? I mean, why did "they" come up with these techniques and what are these useful for?
• can you see if a matrix has an inverse just by looking at it? in other words is there a way to tell if a matrix has an inverse without going through a long process?
• Not all square matrix have an inverse->Requirements to have an Inverse
The matrix must be square (same number of rows and columns).
The determinant of the matrix must not be zero. This is instead of the real number not being zero to have an inverse, the determinant must not be zero to have an inverse. (from http://people.richland.edu/james/lecture/m116/matrices/inverses.html)
• Thank you for your help!
• CAn someone explain how to the inverse of 3x3 matrices going onwards?
• Can an identity matrix not be square?
(1 vote)
• No, the definition of the identity matrix requires that it be square.
• whe can apply this metod to matrix whit 3x3 or more? and how?
• (1/7)[[1,5],[2,6]] does not equal [[1,5],[2,6]]/7? Wouldn't that be matrix division?
• What about a matrix filled entirely with ones or any other number for that matter? Will that not give you undefined behavior IE division by zero?
• No, if you multiply by a matrix filled with 1's, you get a new matrix of values. Say you have a 3 x 3 matrix of values
[ 2 -2 4 ]
| 1 3 9 |
[-4 8 .5 ]
If you multiply by a 3 x 3 matrix of 1's your result (product) is
[ 4 4 4 ]
| 13 13 13 |
[4.5 4.5 4.5 ]

If you multiply the other direction (all 1's matrix first) you get another perfectly good product matrix
[ -1 9 13.5 ]
| -1 9 13.5 |
[ -1 9 13.5 ]

If you multiply the same beginning matrix by an all -2's matrix, you get another perfectly good product matrix
[ -8 -8 -8]
| -26 -26 -26 |
[ -9 -9 -9 ]
(1 vote)