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. = -73 Ex Evaluate -3 -2 0 1 2 = (2*0*6 + -3*3*1 + 4*-2*2) ---- (1*0*4 =
(2*0*6 +
-3*3*1 +
4*-2*2)
----
(1*0*4
+ 2*3*2
+ 6*-2*-3)
Step 1: recopy the first two columns.
= ( ) – ( )
Step 2: multiply the
down diagonals and
add the products. =
Step 3: multiply the
up diagonals and
add the products
NOTE: You subtract the up diagonal from the down diagonal
= -73

8. Ex
Evaluate.
det
= -89

9. 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?

10. 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?

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

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

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

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

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

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

17. 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!

18. Homework:
***Worksheet***
1.3