1. Bellwork 1) Multiply. 3) Find the determinant. 2) Multiply.

2. Answers

3. 3.8A Use Inverse Matrices to solve linear systems
Algebra II

4. Identity In other words, 5 * __= 5? What does “identity” mean to you?
What is the multiplicative identity for the real numbers?
In other words, 5 * __= 5?
The identity for multiplication is 1 because anything multiplied by 1 will be itself.

5. a * a-1= 1 In other words, 5 * ___=1?
What do we multiply by to get the identity?
In other words, 5 * ___=1?
a * a-1= 1
Any number multiplied by its inverse will be the identity.

6. A * A-1= I A-1 *A = I Identity Matrix
Any matrix multiplied by its inverse will be the identity matrix.
A * A-1= I
A-1 *A = I
2x2 Identity Matrix

7. Identity Matrix
Just like 5*1 = 5…
AI= A
IA= A Or

8. Determine whether A and B are inverses.
Find out if AB = I
If so, then yes they’re inverses.
If not, then no they’re not inverses.
Use your calculator.
YES

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

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

11. Ex. 2 Find A-1, if it exists.
Does not exist, because it’s not square.

12. Solving Matrix Equations
Suppose ax = b
How do you solve for x?
We cannot divide matrices, but we can multiply by the inverse.
A-1
AX = B
A-1
IX = A-1B
X = A-1B

13. Ex. 3 Solving a Matrix Equation
Solve the matrix equation AX=B for the 2x2 matrix X

14. Step 2: Multiply both sides of the equation
Step 1: find A-1
A-1=
Step 2: Multiply both sides of the equation
By A-1 on the left

15. You can check the
Solution by mult
AX to see if you get B

16. Assignment

17. Inverses What does “inverse” mean to you?
What is the inverse of multiplication?

18. Determine whether A and B are inverses.NO