LU BIBLE Math 101 – Linear Algebra By: Abdulsalam Shalashtein
Preview:
Citation preview
- Slide 1
- LU BIBLE Math 101 Linear Algebra By: Abdulsalam
Shalashtein
- Slide 2
- Slide 3
- Row 1 Row 2 Column 1Column 2Column 3 Entries
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Lower TriangularUpper Triangular Diagonal Matrix
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Now for this part I will illustrate how to multiply matrices,
but this isnt to be used for proper mathematical writing this is
only to get y to understand the concept. Proceed to the next
slide.
- 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...
- Slide 15
- I do these by stacking The answer goes here. Let's use these
matrices: Let's find :
- Slide 16
- We just do an intersecting row and column thing: To fill this
spot, we multiply and add:
- Slide 17
- Each entry in the answer matrix will work like this...
- Slide 18
- Slide 19
- So the answer is : Now Can we Multiply A B ?
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 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