Status: Tags: #cards/math232/unit3 Links: Matrix
Matrix Inverse
Principles
?
- Not all matrices have an inverse
- Matrix inverses are unique
General form for 2x2
?
- ad - bc != 0 is deteriminant
- If ad-bc = 0 then no inverse
-
- Turns A to I
- Turns I to $A^{-1}$
In relation to matrix A and B
? If A is a matrix and B is a matrix such that AB = I, then B is inverse of A, denoted $A^{-1}$
- I is standard basis matrix / multiplicative matrix
Properties
Finding general form for matrix inverse
?
- Solve for
-
- Distribute using matrix multiplication to create a system for each column in x
- you can use letter variables as a scalar
-
Invertible Matrix Theorem
?
Inverse Linear Mappings
?
- If you have the inverse of the matrix, you can find the inverse linear mapping
-
- Inverse maps
-
Examples
?
- Turn LHS into identity matrix, right will be inverse
-
- Check by A(B) = I?
Find x in for AX=B
Find x in for XA=B
X = B$A^{-1}$
Backlinks
|
|
References:
Created:: 2022-02-05 17:53