InverseMatrix.md (727B)
1 # Inverse Matrix 2 3 **Source:** Strang Lectures 4 5 **Lecture:** 2 6 7 **Definition:** The inverse matrix is the matrix such that A * A' = I. 8 9 ## Example 10 11 Find inverse of M. 12 13 M = [ 1 0 0] 14 [-3 1 0] 15 [ 0 0 1] 16 17 SOLVING: 18 19 M' [ 1 0 0] = [1 0 0] 20 [-3 1 0] [0 1 0] 21 [ 0 0 1] [0 0 1] 22 23 M' = [1 0 0] 24 [3 1 0] 25 [0 0 1] 26 27 To solve for the inverse of a matrix we can create an inequality between A and I (or better would be an augmented matrix). 28 We then make changes to both sides such that the left side of the inequality becomes the identity matrix. What was 29 formerly the identity matrix is now the inverse matrix because those are the transformations required to convert from 30 A to the identity matrix, hence A^-1 A = I.