1. What would happen to this problem if there weren’t parentheses?
Warm Up
Solve for x and y:
What would happen to this problem if there weren’t parentheses?
**Watch your signs**

2. Determinants
&
Inverses

3. A real number associated with any square matrix A, denoted by
Determinants
A real number associated with any square matrix A, denoted by
detA or |A|

4. Determinant of a 2x2
- cb
= ad

5. Ex. Evaluate the determinant:
=1(7)
— 2(4)
= 7 - 8
= -1

6. Ex. Evaluate the determinant:
=7(3)
- 2(-2) =
= 25

7. What can I add to a matrix by to keep it the same?
What is an ADDITIVE…..
IDENTITY:
What can I add to a matrix by to keep it the same?

8. What can I add to a matrix to eliminate all elements?
What is an ADDITIVE…..
INVERSE:
What can I add to a matrix to eliminate all elements?

9. What is a MULTIPLICATIVE…..
IDENTITY:
What can I multiply a matrix by to keep it the same?
***We call this the IDENTITY matrix***

10. What is a MULTIPLICATIVE…..
INVERSE:
What can I multiply a matrix by to get the Identity Matrix?
*** Multiplicative Inverse = ***

11. How do I actually find the Inverse Matrix?
You need to find the determinant!!!

12. The Inverse of a 2x2 Matrix
***If ad-cb=0, then the matrix has no inverse!!!!
A-1=
As long as ad-cb =0

13. Ex. Find A-1, if it exists.
A-1=

14. Ex. Find A-1, if it exists.
A-1=

15. A-1= Does not exist, because it’s not a square matrix!
Ex. Find A-1, if it exists.
NOT POSSIBLE
A-1= Does not exist, because it’s not a square matrix!

16. Homework:
***Worksheet***
1.3