1. LU BIBLE Math 101 – Linear Algebra By: Abdulsalam Shalashtein

3. Row 1 Row 2 Column 1Column 2Column 3 Entries

8. Lower TriangularUpper Triangular Diagonal Matrix

13.  Now for this part I will illustrate how to multiply matrices, but this isn’t to be used for proper mathematical writing this is only to get y to understand the concept. Proceed to the next slide.

14. Here's how it works: Say the size of matrix A is 3 x 4 and the size of matrix B is 4 x 1 and we want... Looking at the sizes...

15. I do these by stacking The answer goes here. Let's use these matrices: Let's find :

16. We just do an intersecting row and column thing: To fill this spot, we multiply and add:

17. Each entry in the answer matrix will work like this...

19. So the answer is : Now Can we Multiply A ▪ B ?

24.  A matrix A is said to be invertible ( non-singular) if there exists a matrix B where AB=BA=I n  If A and B are invertible then : (AB) -1 = B -1 A -1  A 1, …, A r are (nxn) invertible matrices, then A 1 x … x A r is invertible and (A 1 x … x A r )-1 = A r -1 x … x A 1 -1